{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-g7","topicId":"scwiki-topic-g7","code":"G7","slug":"spin-liquids-and-superconductivity","title":"Spin liquids, RVB and superconductivity","summary":"Compare NMR, ESR and transport evidence for a spin-liquid candidate, separating defects, model-dependent gaps and neighboring superconductivity.","aliases":["quantum spin liquid","QSL","resonating valence bond","RVB","kappa BEDT TTF","organic superconductors","κ-(BEDT-TTF)₂Cu₂(CN)₃"],"evidenceTypes":["hypothesis","theory","experiment"],"relatedCodes":["B9","D3","C2","H2"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-18T16:13:01.112201+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Shimizu author methods/figures, Miksch author methods/supplement figure, Pustogow final passages and scoped historical abstracts; independent singlet-triplet/background checks.","limitations":["Complete scientific acceptance remains open.","Full final-version comparison, raw-data reproduction and complete calibration remain incomplete.","A spin gap or missing magnetic order alone does not identify a quantum spin liquid.","The independent finite dimer/background is not a material fit or a bulk topological-state simulation."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"G_magnetism_interplay/G7_spin_liquid_SC.md","sha256":"c290c1c28c6e96cc7734f29527752a2a352e46b552acfa7251562dbb9b84ae7f","sourceId":"file-398c5d564623ddd7"},"sourceMap":[{"startLine":1,"endLine":28,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":29,"endLine":119,"targetSections":["mathematical-assumptions"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":120,"endLine":171,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":172,"endLine":219,"targetSections":["experimental-criteria"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":220,"endLine":260,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":261,"endLine":300,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":301,"endLine":339,"targetSections":["limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":340,"endLine":383,"targetSections":["limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":384,"endLine":453,"targetSections":[],"decision":"not-published-as-scientific-evidence","note":"Historical audit scores and repeated summaries are not scientific verification. Selected cautions are rewritten in the limits section."},{"startLine":454,"endLine":468,"targetSections":["limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":469,"endLine":560,"targetSections":[],"decision":"not-published-as-scientific-evidence","note":"Historical audit scores and repeated summaries are not scientific verification. Selected cautions are rewritten in the limits section."}],"corrections":[{"id":"scwiki-g7-correction-1","description":"The source's categorical QSL taxonomy and BCS-versus-RVB summary are narrowed. Absence of order is not a QSL proof, a generic U(1) spin liquid is not necessarily a Dirac state, and BCS mean-field language does not specify a phonon-only mechanism.","sourceId":"source-5a6026d6455bf7a0","scope":"Conceptual editorial correction; no new material-level QSL assignment."},{"id":"scwiki-g7-correction-2","description":"Keep 32mK measurement floor,250K exchange scale,6K anomaly and distinct ESR/transport gap estimates separate. No universal relaxation exponent or pressure-to-superconductivity mechanism is inferred.","sourceId":"source-5e0dcd80e8b64a1b","scope":"Selected primary methods and final transport-versus-ESR distinction."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}","check":"5 independent central-derivative checks and15 synthetic background cases passed. Units kB=gmuB=1; no material fit or intrinsic gapless-state diagnosis."}],"references":[{"id":"source-5a6026d6455bf7a0","doi":"10.1126/science.235.4793.1196","title":"The Resonating Valence Bond State in La2CuO4 and Superconductivity","year":1987,"url":"https://doi.org/10.1126/science.235.4793.1196","publicationStatus":"journal-article","verification":{"scope":"indexed-primary-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://pubmed.ncbi.nlm.nih.gov/17818979/","note":"Original abstract at PubMed: historical proposal, not a confirmed parent-state diagnosis. Publisher endpoint unavailable; full text not checked."}},{"id":"source-9d15cd9236072f5c","doi":"10.1103/PhysRevLett.91.107001","title":"Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice","year":2003,"url":"https://doi.org/10.1103/PhysRevLett.91.107001","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figures","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0307483v1","note":"Author version submitted19July2003, selectedpp1–4 andp2Figures2–3 visually checked. 32mK at2.2T singlecrystal,0.4K two-component recovery and comparison-based moment estimate retained; final/raw-data audit incomplete. Internal2018typesetting date is not publication."}},{"id":"source-0443485ac20d3a8c","doi":"10.1103/PhysRevLett.95.177001","title":"Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3","year":2005,"url":"https://doi.org/10.1103/PhysRevLett.95.177001","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://link.aps.org/doi/10.1103/PhysRevLett.95.177001","note":"Pressure NMR/resistivity phase diagram and neighboring superconductivity; no causal RVB mechanism established. Full data not reviewed."}},{"id":"source-5e0dcd80e8b64a1b","doi":"10.1038/s41467-023-37491-z","title":"Chasing the spin gap through the phase diagram of a frustrated Mott insulator","year":2023,"url":"https://doi.org/10.1038/s41467-023-37491-z","publicationStatus":"journal-article","verification":{"scope":"published-primary-passages-scoped-check","checkedAt":"2026-10-19","evidenceUrl":"https://www.nature.com/articles/s41467-023-37491-z.pdf","note":"Published pp.1–5 selected results,discussion,methods and data analysis; Fig4/discussion visually checked. Substrate strain and inferred hydrostatic-equivalent pressure, VBS interpretation with gapped chiral QSL not excluded, mounting microcracks retained. Raw-data audit pending. Finalp3 explicitly distinguishes transport Eg=2Delta approximately30–50K from ESR spin gap12K; these are different probes, not a demonstrated manuscript-version conflict."}},{"id":"source-ef796739e836bb78","doi":"10.1126/science.abc6363","title":"Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3","year":2021,"url":"https://doi.org/10.1126/science.abc6363","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-supplement-figure","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/2010.16155v1","note":"Authorv1 submitted30October2020; selectedmainpp3,5–6,S1/S2methods andsupplementS2B/PDF20–21 read; PDF20FigureS5 visually checked. Plainactivated7.3K versus chainfit12.1K are model-dependent. Maintext/legend include inverse-Tprefactor whereas printedS3 omits it; no silent repair or full-final reproduction. Finalindexedabstract/pubdate16April2021 checked separately atPubMed33859031."}}],"materialCases":[{"formula":"κ-(BEDT-TTF)2Cu2(CN)3","sample":"frustrated organic Mott system under pressure","recordType":"experiment","tcK":null,"temperatureNote":"source notes describe a few-kelvin superconducting phase; exact criterion not re-extracted","criterion":"unknown","pressureRegime":"high","pressureGPa":null,"equilibrium":"unknown","probe":"pressure-dependent phase diagram","id":"scwiki-g7-material-1","sourceId":"source-0443485ac20d3a8c","reportedTemperatureK":null,"temperatureKind":"unassigned","aliases":["organic","organic superconductors"]},{"id":"scwiki-g7-material-2","formula":"κ-(BEDT-TTF)2Cu2(CN)3","sample":"Shimizu single crystal under2.2T perpendicular to conducting planes","recordType":"experiment","reportedTemperatureK":0.032,"tcK":null,"temperatureKind":"measurement","temperatureNote":"Lowest proton NMR measurement temperature at2.2T; not zero field, an exchange scale or a superconducting Tc.","criterion":"NMR-order-bound","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Proton nuclear magnetic resonance","sourceId":"source-9d15cd9236072f5c","aliases":["organic Mott insulator"]}],"claims":[{"id":"scwiki-g7-claim-scope-1","sectionId":"scope","statement":"A quantum spin liquid is not identified simply by an absence of detected magnetic order. A candidate material must be tested against valence-bond order, disorder, freezing and the finite temperature and time windows of the measurements. A spin gap can occur in different states; its observation alone does not identify topological order or fractionalized excitations. Here the organic Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 illustrates how interpretations change when additional probes become available.","evidenceType":"hypothesis","sourceIds":["source-9d15cd9236072f5c","source-5e0dcd80e8b64a1b","source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-scope-2","sectionId":"scope","statement":"RVB, or resonating valence bond, describes a family of theoretical constructions built from superpositions of singlet configurations. Anderson's cuprate proposal connects this idea to superconductivity in a doped correlated insulator; the abstract is a historical proposal, not a material-level proof of a spin-liquid parent. The allowed coverings, amplitudes and constraints must be specified. A generic U(1) construction is not automatically a Dirac state, and BCS mean-field language does not imply a phonon-only pairing interaction.","evidenceType":"hypothesis","sourceIds":["source-5a6026d6455bf7a0"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"An independent finite example makes one logical limitation explicit. Consider an isolated singlet of energy zero and three triplet states with energies $\\Delta-h$, $\\Delta$ and $\\Delta+h$. Use units $k_B=g\\mu_B=1$, so temperatures, gaps and the field variable h are expressed in compatible energy units; the response below is not an SI molar susceptibility. The partition function is $Z=1+e^{-\\Delta/T}[1+2\\cosh(h/T)]$. Differentiating the mean moment at zero field gives $\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}$. This illustrative model addresses an inference problem raised by the magnetic measurements, rather than fitting those experiments.","evidenceType":"theory","sourceIds":["source-9d15cd9236072f5c","source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"The model has a gap and a nonmagnetic singlet ground state, yet an isolated dimer has neither bulk topological order nor mobile charge. Adding a synthetic Curie contribution gives $\\chi_{\\mathrm{obs}}=\\chi_0+c/T$. With an illustrative gap of 6 K, c = 0.001 and T = 0.1 K, the background exceeds 99.9999% of the total response even though the intrinsic response is exponentially suppressed. The chosen 6 K is a model parameter, not the measured anomaly temperature or a fitted material gap. An inverse-temperature tail cannot by itself establish a gapless intrinsic state.","evidenceType":"theory","sourceIds":["source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Five finite-difference derivatives agree with the analytic response, and fifteen temperature/background combinations check this counterexample. Its Curie term assumes independent, unsaturated moments; interactions, anisotropy and finite-field saturation are excluded. Singlet correlations in an insulating model also do not demonstrate charge coherence or superconductivity. The separate [RVB discussion](/scwiki/rvb-and-doped-mott-insulators) examines wavefunction normalization and charge-response assumptions. These finite calculations are not a simulation of a bulk quantum spin liquid.","evidenceType":"theory","sourceIds":["source-5a6026d6455bf7a0","source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Shimizu and colleagues' lowest-temperature proton NMR measurements used a single crystal at 2.2 T perpendicular to the conducting planes, reaching 32 mK. That temperature floor is not a zero-field result. Their higher-temperature polycrystalline NMR used 3.9 T, and susceptibility measurements used 0.32 T. No resolved splitting or major broadening was observed at low temperature, but the small-moment estimate relies on calibration against a different chloride salt. The absence of a resolved signal therefore has a probe- and model-dependent bound.","evidenceType":"experiment","sourceIds":["source-9d15cd9236072f5c"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Below approximately 0.4 K, the reported recovery needs two exponential components, with roughly linear and quadratic temperature dependences of their relaxation rates. The authors discuss spatial inhomogeneity and possible disorder-related explanations. Combining these components into one universal power law would discard relevant evidence. The approximately 250 K exchange scale obtained from the susceptibility analysis is neither the 32 mK measurement floor nor a superconducting transition temperature.","evidenceType":"experiment","sourceIds":["source-9d15cd9236072f5c"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Miksch and colleagues separate a decreasing main ESR contribution below the approximately 6 K anomaly from narrow defect-related components. Their author manuscript uses conventional 9.5 GHz measurements near 340 mT down to 1.9 K, alongside separate low-frequency measurements near 40 mT reaching 25 mK. These are different protocols, not one continuous zero-field measurement. Samples from four laboratories show different defect signals. The proposed microscopic defect origin remains an interpretation; the final abstract describes a gapped ground state consistent with a valence-bond solid.","evidenceType":"experiment","sourceIds":["source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Gap values require their observable and fitting model. Miksch's author supplement compares a simple activated fit giving 7.3 K with a chain-based fit giving 12.1 K. Its main text and figure legend include an inverse-temperature prefactor that the displayed supplementary expression omits; no unreported correction or independent reproduction of that fit is claimed here. Pustogow's final paper explicitly distinguishes its transport scale $E_g=2\\Delta\\approx30$–50 K from the approximately 12 K ESR spin gap. These numbers are not interchangeable measurements of one quantity, nor evidence by themselves of a manuscript-version error.","evidenceType":"hypothesis","sourceIds":["source-5e0dcd80e8b64a1b","source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"The strain-transport study favors a valence-bond-solid interpretation but leaves a gapped chiral spin liquid possible. Its hydrostatic-equivalent pressure is inferred for a substrate-coupled crystal; it is not a directly applied hydrostatic pressure. Kurosaki's pressure phase diagram establishes neighboring electronic phases and superconductivity, but proximity does not identify the pairing mediator. Complete scientific acceptance remains open: final-version comparisons, raw-data analysis, full calibration and discrimination among microscopic states are incomplete. Reference labels identify which selected methods, figures or abstracts were actually checked.","evidenceType":"hypothesis","sourceIds":["source-0443485ac20d3a8c","source-5e0dcd80e8b64a1b","source-ef796739e836bb78"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."},{"id":"scwiki-g7-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Record the sample, magnetic field, frequency or time window, temperature floor, background subtraction and fitting assumptions for each proposed spin-liquid signature. Compare magnetic, structural, thermodynamic and charge-coherence observations under compatible conditions. A useful mechanism proposal must predict observations that distinguish alternatives across the transition, including the behavior of defects. Superconductivity next to a candidate insulating state motivates such tests; it does not establish fractionalization-mediated pairing.","evidenceType":"hypothesis","sourceIds":["source-9d15cd9236072f5c","source-0443485ac20d3a8c","source-5e0dcd80e8b64a1b"],"conditions":"Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.","verificationScope":"Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open."}],"body":"## Scope\n\nA quantum spin liquid is not identified simply by an absence of detected magnetic order. A candidate material must be tested against valence-bond order, disorder, freezing and the finite temperature and time windows of the measurements. A spin gap can occur in different states; its observation alone does not identify topological order or fractionalized excitations. Here the organic Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 illustrates how interpretations change when additional probes become available. [R2](#ref-source-9d15cd9236072f5c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nRVB, or resonating valence bond, describes a family of theoretical constructions built from superpositions of singlet configurations. Anderson's cuprate proposal connects this idea to superconductivity in a doped correlated insulator; the abstract is a historical proposal, not a material-level proof of a spin-liquid parent. The allowed coverings, amplitudes and constraints must be specified. A generic U(1) construction is not automatically a Dirac state, and BCS mean-field language does not imply a phonon-only pairing interaction. [R1](#ref-source-5a6026d6455bf7a0)\n\n## Mathematical assumptions\n\nAn independent finite example makes one logical limitation explicit. Consider an isolated singlet of energy zero and three triplet states with energies $\\Delta-h$, $\\Delta$ and $\\Delta+h$. Use units $k_B=g\\mu_B=1$, so temperatures, gaps and the field variable h are expressed in compatible energy units; the response below is not an SI molar susceptibility. The partition function is $Z=1+e^{-\\Delta/T}[1+2\\cosh(h/T)]$. Differentiating the mean moment at zero field gives $\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}$. This illustrative model addresses an inference problem raised by the magnetic measurements, rather than fitting those experiments. [R2](#ref-source-9d15cd9236072f5c) [R5](#ref-source-ef796739e836bb78)\n\nThe model has a gap and a nonmagnetic singlet ground state, yet an isolated dimer has neither bulk topological order nor mobile charge. Adding a synthetic Curie contribution gives $\\chi_{\\mathrm{obs}}=\\chi_0+c/T$. With an illustrative gap of 6 K, c = 0.001 and T = 0.1 K, the background exceeds 99.9999% of the total response even though the intrinsic response is exponentially suppressed. The chosen 6 K is a model parameter, not the measured anomaly temperature or a fitted material gap. An inverse-temperature tail cannot by itself establish a gapless intrinsic state. [R5](#ref-source-ef796739e836bb78)\n\nFive finite-difference derivatives agree with the analytic response, and fifteen temperature/background combinations check this counterexample. Its Curie term assumes independent, unsaturated moments; interactions, anisotropy and finite-field saturation are excluded. Singlet correlations in an insulating model also do not demonstrate charge coherence or superconductivity. The separate [RVB discussion](/scwiki/rvb-and-doped-mott-insulators) examines wavefunction normalization and charge-response assumptions. These finite calculations are not a simulation of a bulk quantum spin liquid. [R1](#ref-source-5a6026d6455bf7a0) [R5](#ref-source-ef796739e836bb78)\n\n## Experimental criteria\n\nShimizu and colleagues' lowest-temperature proton NMR measurements used a single crystal at 2.2 T perpendicular to the conducting planes, reaching 32 mK. That temperature floor is not a zero-field result. Their higher-temperature polycrystalline NMR used 3.9 T, and susceptibility measurements used 0.32 T. No resolved splitting or major broadening was observed at low temperature, but the small-moment estimate relies on calibration against a different chloride salt. The absence of a resolved signal therefore has a probe- and model-dependent bound. [R2](#ref-source-9d15cd9236072f5c)\n\nBelow approximately 0.4 K, the reported recovery needs two exponential components, with roughly linear and quadratic temperature dependences of their relaxation rates. The authors discuss spatial inhomogeneity and possible disorder-related explanations. Combining these components into one universal power law would discard relevant evidence. The approximately 250 K exchange scale obtained from the susceptibility analysis is neither the 32 mK measurement floor nor a superconducting transition temperature. [R2](#ref-source-9d15cd9236072f5c)\n\nMiksch and colleagues separate a decreasing main ESR contribution below the approximately 6 K anomaly from narrow defect-related components. Their author manuscript uses conventional 9.5 GHz measurements near 340 mT down to 1.9 K, alongside separate low-frequency measurements near 40 mT reaching 25 mK. These are different protocols, not one continuous zero-field measurement. Samples from four laboratories show different defect signals. The proposed microscopic defect origin remains an interpretation; the final abstract describes a gapped ground state consistent with a valence-bond solid. [R5](#ref-source-ef796739e836bb78)\n\n## Limits and disputes\n\nGap values require their observable and fitting model. Miksch's author supplement compares a simple activated fit giving 7.3 K with a chain-based fit giving 12.1 K. Its main text and figure legend include an inverse-temperature prefactor that the displayed supplementary expression omits; no unreported correction or independent reproduction of that fit is claimed here. Pustogow's final paper explicitly distinguishes its transport scale $E_g=2\\Delta\\approx30$–50 K from the approximately 12 K ESR spin gap. These numbers are not interchangeable measurements of one quantity, nor evidence by themselves of a manuscript-version error. [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nThe strain-transport study favors a valence-bond-solid interpretation but leaves a gapped chiral spin liquid possible. Its hydrostatic-equivalent pressure is inferred for a substrate-coupled crystal; it is not a directly applied hydrostatic pressure. Kurosaki's pressure phase diagram establishes neighboring electronic phases and superconductivity, but proximity does not identify the pairing mediator. Complete scientific acceptance remains open: final-version comparisons, raw-data analysis, full calibration and discrimination among microscopic states are incomplete. Reference labels identify which selected methods, figures or abstracts were actually checked. [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\n## Discovery implications\n\nRecord the sample, magnetic field, frequency or time window, temperature floor, background subtraction and fitting assumptions for each proposed spin-liquid signature. Compare magnetic, structural, thermodynamic and charge-coherence observations under compatible conditions. A useful mechanism proposal must predict observations that distinguish alternatives across the transition, including the behavior of defects. Superconductivity next to a candidate insulating state motivates such tests; it does not establish fractionalization-mediated pairing. [R2](#ref-source-9d15cd9236072f5c) [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b)\n\n## Related topics\n\n[RVB and doped Mott insulators](/scwiki/rvb-and-doped-mott-insulators), [cuprates](/scwiki/cuprates), [gap-sign constraints](/scwiki/s-plus-minus), and [normal-state dissipation](/scwiki/planckian-dissipation).","revision":"ac215be3b2636cf6e38d","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nA quantum spin liquid is not identified simply by an absence of detected magnetic order. A candidate material must be tested against valence-bond order, disorder, freezing and the finite temperature and time windows of the measurements. A spin gap can occur in different states; its observation alone does not identify topological order or fractionalized excitations. Here the organic Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 illustrates how interpretations change when additional probes become available. [R2](#ref-source-9d15cd9236072f5c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nRVB, or resonating valence bond, describes a family of theoretical constructions built from superpositions of singlet configurations. Anderson's cuprate proposal connects this idea to superconductivity in a doped correlated insulator; the abstract is a historical proposal, not a material-level proof of a spin-liquid parent. The allowed coverings, amplitudes and constraints must be specified. A generic U(1) construction is not automatically a Dirac state, and BCS mean-field language does not imply a phonon-only pairing interaction. [R1](#ref-source-5a6026d6455bf7a0)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nAn independent finite example makes one logical limitation explicit. Consider an isolated singlet of energy zero and three triplet states with energies $\\Delta-h$, $\\Delta$ and $\\Delta+h$. Use units $k_B=g\\mu_B=1$, so temperatures, gaps and the field variable h are expressed in compatible energy units; the response below is not an SI molar susceptibility. The partition function is $Z=1+e^{-\\Delta/T}[1+2\\cosh(h/T)]$. Differentiating the mean moment at zero field gives $\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}$. This illustrative model addresses an inference problem raised by the magnetic measurements, rather than fitting those experiments. [R2](#ref-source-9d15cd9236072f5c) [R5](#ref-source-ef796739e836bb78)\n\nThe model has a gap and a nonmagnetic singlet ground state, yet an isolated dimer has neither bulk topological order nor mobile charge. Adding a synthetic Curie contribution gives $\\chi_{\\mathrm{obs}}=\\chi_0+c/T$. With an illustrative gap of 6 K, c = 0.001 and T = 0.1 K, the background exceeds 99.9999% of the total response even though the intrinsic response is exponentially suppressed. The chosen 6 K is a model parameter, not the measured anomaly temperature or a fitted material gap. An inverse-temperature tail cannot by itself establish a gapless intrinsic state. [R5](#ref-source-ef796739e836bb78)\n\nFive finite-difference derivatives agree with the analytic response, and fifteen temperature/background combinations check this counterexample. Its Curie term assumes independent, unsaturated moments; interactions, anisotropy and finite-field saturation are excluded. Singlet correlations in an insulating model also do not demonstrate charge coherence or superconductivity. The separate [RVB discussion](/scwiki/rvb-and-doped-mott-insulators) examines wavefunction normalization and charge-response assumptions. These finite calculations are not a simulation of a bulk quantum spin liquid. [R1](#ref-source-5a6026d6455bf7a0) [R5](#ref-source-ef796739e836bb78)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nShimizu and colleagues' lowest-temperature proton NMR measurements used a single crystal at 2.2 T perpendicular to the conducting planes, reaching 32 mK. That temperature floor is not a zero-field result. Their higher-temperature polycrystalline NMR used 3.9 T, and susceptibility measurements used 0.32 T. No resolved splitting or major broadening was observed at low temperature, but the small-moment estimate relies on calibration against a different chloride salt. The absence of a resolved signal therefore has a probe- and model-dependent bound. [R2](#ref-source-9d15cd9236072f5c)\n\nBelow approximately 0.4 K, the reported recovery needs two exponential components, with roughly linear and quadratic temperature dependences of their relaxation rates. The authors discuss spatial inhomogeneity and possible disorder-related explanations. Combining these components into one universal power law would discard relevant evidence. The approximately 250 K exchange scale obtained from the susceptibility analysis is neither the 32 mK measurement floor nor a superconducting transition temperature. [R2](#ref-source-9d15cd9236072f5c)\n\nMiksch and colleagues separate a decreasing main ESR contribution below the approximately 6 K anomaly from narrow defect-related components. Their author manuscript uses conventional 9.5 GHz measurements near 340 mT down to 1.9 K, alongside separate low-frequency measurements near 40 mT reaching 25 mK. These are different protocols, not one continuous zero-field measurement. Samples from four laboratories show different defect signals. The proposed microscopic defect origin remains an interpretation; the final abstract describes a gapped ground state consistent with a valence-bond solid. [R5](#ref-source-ef796739e836bb78)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nGap values require their observable and fitting model. Miksch's author supplement compares a simple activated fit giving 7.3 K with a chain-based fit giving 12.1 K. Its main text and figure legend include an inverse-temperature prefactor that the displayed supplementary expression omits; no unreported correction or independent reproduction of that fit is claimed here. Pustogow's final paper explicitly distinguishes its transport scale $E_g=2\\Delta\\approx30$–50 K from the approximately 12 K ESR spin gap. These numbers are not interchangeable measurements of one quantity, nor evidence by themselves of a manuscript-version error. [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nThe strain-transport study favors a valence-bond-solid interpretation but leaves a gapped chiral spin liquid possible. Its hydrostatic-equivalent pressure is inferred for a substrate-coupled crystal; it is not a directly applied hydrostatic pressure. Kurosaki's pressure phase diagram establishes neighboring electronic phases and superconductivity, but proximity does not identify the pairing mediator. Complete scientific acceptance remains open: final-version comparisons, raw-data analysis, full calibration and discrimination among microscopic states are incomplete. Reference labels identify which selected methods, figures or abstracts were actually checked. [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nRecord the sample, magnetic field, frequency or time window, temperature floor, background subtraction and fitting assumptions for each proposed spin-liquid signature. Compare magnetic, structural, thermodynamic and charge-coherence observations under compatible conditions. A useful mechanism proposal must predict observations that distinguish alternatives across the transition, including the behavior of defects. Superconductivity next to a candidate insulating state motivates such tests; it does not establish fractionalization-mediated pairing. [R2](#ref-source-9d15cd9236072f5c) [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\n[RVB and doped Mott insulators](/scwiki/rvb-and-doped-mott-insulators), [cuprates](/scwiki/cuprates), [gap-sign constraints](/scwiki/s-plus-minus), and [normal-state dissipation](/scwiki/planckian-dissipation)."},{"id":"material-cases","title":"Material cases","markdown":"## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| κ-(BEDT-TTF)2Cu2(CN)3 (aliases: organic, organic superconductors); frustrated organic Mott system under pressure | source notes describe a few-kelvin superconducting phase; exact criterion not re-extracted | unassigned; unknown | pressure-dependent phase diagram | high; unknown GPa | unknown | experiment; [source](#ref-source-0443485ac20d3a8c) |\n| κ-(BEDT-TTF)2Cu2(CN)3 (aliases: organic Mott insulator); Shimizu single crystal under2.2T perpendicular to conducting planes | 0.032 K; Lowest proton NMR measurement temperature at2.2T; not zero field, an exchange scale or a superconducting Tc. | measurement; NMR-order-bound | Proton nuclear magnetic resonance | ambient; unknown GPa | unknown | experiment; [source](#ref-source-9d15cd9236072f5c) |"}],"markdown":"# Spin liquids, RVB and superconductivity\n\nCompare NMR, ESR and transport evidence for a spin-liquid candidate, separating defects, model-dependent gaps and neighboring superconductivity.\n\n## Scope\n\nA quantum spin liquid is not identified simply by an absence of detected magnetic order. A candidate material must be tested against valence-bond order, disorder, freezing and the finite temperature and time windows of the measurements. A spin gap can occur in different states; its observation alone does not identify topological order or fractionalized excitations. Here the organic Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 illustrates how interpretations change when additional probes become available. [R2](#ref-source-9d15cd9236072f5c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nRVB, or resonating valence bond, describes a family of theoretical constructions built from superpositions of singlet configurations. Anderson's cuprate proposal connects this idea to superconductivity in a doped correlated insulator; the abstract is a historical proposal, not a material-level proof of a spin-liquid parent. The allowed coverings, amplitudes and constraints must be specified. A generic U(1) construction is not automatically a Dirac state, and BCS mean-field language does not imply a phonon-only pairing interaction. [R1](#ref-source-5a6026d6455bf7a0)\n\n## Mathematical assumptions\n\nAn independent finite example makes one logical limitation explicit. Consider an isolated singlet of energy zero and three triplet states with energies $\\Delta-h$, $\\Delta$ and $\\Delta+h$. Use units $k_B=g\\mu_B=1$, so temperatures, gaps and the field variable h are expressed in compatible energy units; the response below is not an SI molar susceptibility. The partition function is $Z=1+e^{-\\Delta/T}[1+2\\cosh(h/T)]$. Differentiating the mean moment at zero field gives $\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}$. This illustrative model addresses an inference problem raised by the magnetic measurements, rather than fitting those experiments. [R2](#ref-source-9d15cd9236072f5c) [R5](#ref-source-ef796739e836bb78)\n\nThe model has a gap and a nonmagnetic singlet ground state, yet an isolated dimer has neither bulk topological order nor mobile charge. Adding a synthetic Curie contribution gives $\\chi_{\\mathrm{obs}}=\\chi_0+c/T$. With an illustrative gap of 6 K, c = 0.001 and T = 0.1 K, the background exceeds 99.9999% of the total response even though the intrinsic response is exponentially suppressed. The chosen 6 K is a model parameter, not the measured anomaly temperature or a fitted material gap. An inverse-temperature tail cannot by itself establish a gapless intrinsic state. [R5](#ref-source-ef796739e836bb78)\n\nFive finite-difference derivatives agree with the analytic response, and fifteen temperature/background combinations check this counterexample. Its Curie term assumes independent, unsaturated moments; interactions, anisotropy and finite-field saturation are excluded. Singlet correlations in an insulating model also do not demonstrate charge coherence or superconductivity. The separate [RVB discussion](/scwiki/rvb-and-doped-mott-insulators) examines wavefunction normalization and charge-response assumptions. These finite calculations are not a simulation of a bulk quantum spin liquid. [R1](#ref-source-5a6026d6455bf7a0) [R5](#ref-source-ef796739e836bb78)\n\n## Experimental criteria\n\nShimizu and colleagues' lowest-temperature proton NMR measurements used a single crystal at 2.2 T perpendicular to the conducting planes, reaching 32 mK. That temperature floor is not a zero-field result. Their higher-temperature polycrystalline NMR used 3.9 T, and susceptibility measurements used 0.32 T. No resolved splitting or major broadening was observed at low temperature, but the small-moment estimate relies on calibration against a different chloride salt. The absence of a resolved signal therefore has a probe- and model-dependent bound. [R2](#ref-source-9d15cd9236072f5c)\n\nBelow approximately 0.4 K, the reported recovery needs two exponential components, with roughly linear and quadratic temperature dependences of their relaxation rates. The authors discuss spatial inhomogeneity and possible disorder-related explanations. Combining these components into one universal power law would discard relevant evidence. The approximately 250 K exchange scale obtained from the susceptibility analysis is neither the 32 mK measurement floor nor a superconducting transition temperature. [R2](#ref-source-9d15cd9236072f5c)\n\nMiksch and colleagues separate a decreasing main ESR contribution below the approximately 6 K anomaly from narrow defect-related components. Their author manuscript uses conventional 9.5 GHz measurements near 340 mT down to 1.9 K, alongside separate low-frequency measurements near 40 mT reaching 25 mK. These are different protocols, not one continuous zero-field measurement. Samples from four laboratories show different defect signals. The proposed microscopic defect origin remains an interpretation; the final abstract describes a gapped ground state consistent with a valence-bond solid. [R5](#ref-source-ef796739e836bb78)\n\n## Limits and disputes\n\nGap values require their observable and fitting model. Miksch's author supplement compares a simple activated fit giving 7.3 K with a chain-based fit giving 12.1 K. Its main text and figure legend include an inverse-temperature prefactor that the displayed supplementary expression omits; no unreported correction or independent reproduction of that fit is claimed here. Pustogow's final paper explicitly distinguishes its transport scale $E_g=2\\Delta\\approx30$–50 K from the approximately 12 K ESR spin gap. These numbers are not interchangeable measurements of one quantity, nor evidence by themselves of a manuscript-version error. [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\nThe strain-transport study favors a valence-bond-solid interpretation but leaves a gapped chiral spin liquid possible. Its hydrostatic-equivalent pressure is inferred for a substrate-coupled crystal; it is not a directly applied hydrostatic pressure. Kurosaki's pressure phase diagram establishes neighboring electronic phases and superconductivity, but proximity does not identify the pairing mediator. Complete scientific acceptance remains open: final-version comparisons, raw-data analysis, full calibration and discrimination among microscopic states are incomplete. Reference labels identify which selected methods, figures or abstracts were actually checked. [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b) [R5](#ref-source-ef796739e836bb78)\n\n## Discovery implications\n\nRecord the sample, magnetic field, frequency or time window, temperature floor, background subtraction and fitting assumptions for each proposed spin-liquid signature. Compare magnetic, structural, thermodynamic and charge-coherence observations under compatible conditions. A useful mechanism proposal must predict observations that distinguish alternatives across the transition, including the behavior of defects. Superconductivity next to a candidate insulating state motivates such tests; it does not establish fractionalization-mediated pairing. [R2](#ref-source-9d15cd9236072f5c) [R3](#ref-source-0443485ac20d3a8c) [R4](#ref-source-5e0dcd80e8b64a1b)\n\n## Related topics\n\n[RVB and doped Mott insulators](/scwiki/rvb-and-doped-mott-insulators), [cuprates](/scwiki/cuprates), [gap-sign constraints](/scwiki/s-plus-minus), and [normal-state dissipation](/scwiki/planckian-dissipation).\n\n## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| κ-(BEDT-TTF)2Cu2(CN)3 (aliases: organic, organic superconductors); frustrated organic Mott system under pressure | source notes describe a few-kelvin superconducting phase; exact criterion not re-extracted | unassigned; unknown | pressure-dependent phase diagram | high; unknown GPa | unknown | experiment; [source](#ref-source-0443485ac20d3a8c) |\n| κ-(BEDT-TTF)2Cu2(CN)3 (aliases: organic Mott insulator); Shimizu single crystal under2.2T perpendicular to conducting planes | 0.032 K; Lowest proton NMR measurement temperature at2.2T; not zero field, an exchange scale or a superconducting Tc. | measurement; NMR-order-bound | Proton nuclear magnetic resonance | ambient; unknown GPa | unknown | experiment; [source](#ref-source-9d15cd9236072f5c) |\n\n## Sources\n\n### Ref source-5a6026d6455bf7a0\n\n[R1] The Resonating Valence Bond State in La2CuO4 and Superconductivity (1987). [DOI 10.1126/science.235.4793.1196](https://doi.org/10.1126/science.235.4793.1196). Publication: journal-article. Check: indexed-primary-abstract-scoped-check. Checked: 2026-10-18. Original abstract at PubMed: historical proposal, not a confirmed parent-state diagnosis. Publisher endpoint unavailable; full text not checked.\n### Ref source-9d15cd9236072f5c\n\n[R2] Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice (2003). [DOI 10.1103/PhysRevLett.91.107001](https://doi.org/10.1103/PhysRevLett.91.107001). Publication: journal-article. Check: selected-author-methods-and-figures. Checked: 2026-10-19. Author version submitted19July2003, selectedpp1–4 andp2Figures2–3 visually checked. 32mK at2.2T singlecrystal,0.4K two-component recovery and comparison-based moment estimate retained; final/raw-data audit incomplete. Internal2018typesetting date is not publication.\n### Ref source-0443485ac20d3a8c\n\n[R3] Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3 (2005). [DOI 10.1103/PhysRevLett.95.177001](https://doi.org/10.1103/PhysRevLett.95.177001). Publication: journal-article. Check: publisher-abstract-scoped-check. Checked: 2026-10-18. Pressure NMR/resistivity phase diagram and neighboring superconductivity; no causal RVB mechanism established. Full data not reviewed.\n### Ref source-5e0dcd80e8b64a1b\n\n[R4] Chasing the spin gap through the phase diagram of a frustrated Mott insulator (2023). [DOI 10.1038/s41467-023-37491-z](https://doi.org/10.1038/s41467-023-37491-z). Publication: journal-article. Check: published-primary-passages-scoped-check. Checked: 2026-10-19. Published pp.1–5 selected results,discussion,methods and data analysis; Fig4/discussion visually checked. Substrate strain and inferred hydrostatic-equivalent pressure, VBS interpretation with gapped chiral QSL not excluded, mounting microcracks retained. Raw-data audit pending. Finalp3 explicitly distinguishes transport Eg=2Delta approximately30–50K from ESR spin gap12K; these are different probes, not a demonstrated manuscript-version conflict.\n### Ref source-ef796739e836bb78\n\n[R5] Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 (2021). [DOI 10.1126/science.abc6363](https://doi.org/10.1126/science.abc6363). Publication: journal-article. Check: selected-author-methods-and-supplement-figure. Checked: 2026-10-19. Authorv1 submitted30October2020; selectedmainpp3,5–6,S1/S2methods andsupplementS2B/PDF20–21 read; PDF20FigureS5 visually checked. Plainactivated7.3K versus chainfit12.1K are model-dependent. Maintext/legend include inverse-Tprefactor whereas printedS3 omits it; no silent repair or full-final reproduction. Finalindexedabstract/pubdate16April2021 checked separately atPubMed33859031.\n\n## Claim evidence and conditions\n\n### scwiki-g7-claim-scope-1\n\nA quantum spin liquid is not identified simply by an absence of detected magnetic order. A candidate material must be tested against valence-bond order, disorder, freezing and the finite temperature and time windows of the measurements. A spin gap can occur in different states; its observation alone does not identify topological order or fractionalized excitations. Here the organic Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 illustrates how interpretations change when additional probes become available.\n\nEvidence: hypothesis. Sources: source-9d15cd9236072f5c, source-5e0dcd80e8b64a1b, source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-scope-2\n\nRVB, or resonating valence bond, describes a family of theoretical constructions built from superpositions of singlet configurations. Anderson's cuprate proposal connects this idea to superconductivity in a doped correlated insulator; the abstract is a historical proposal, not a material-level proof of a spin-liquid parent. The allowed coverings, amplitudes and constraints must be specified. A generic U(1) construction is not automatically a Dirac state, and BCS mean-field language does not imply a phonon-only pairing interaction.\n\nEvidence: hypothesis. Sources: source-5a6026d6455bf7a0.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-mathematical-assumptions-1\n\nAn independent finite example makes one logical limitation explicit. Consider an isolated singlet of energy zero and three triplet states with energies $\\Delta-h$, $\\Delta$ and $\\Delta+h$. Use units $k_B=g\\mu_B=1$, so temperatures, gaps and the field variable h are expressed in compatible energy units; the response below is not an SI molar susceptibility. The partition function is $Z=1+e^{-\\Delta/T}[1+2\\cosh(h/T)]$. Differentiating the mean moment at zero field gives $\\chi_0=2e^{-\\Delta/T}/\\{T[1+3e^{-\\Delta/T}]\\}$. This illustrative model addresses an inference problem raised by the magnetic measurements, rather than fitting those experiments.\n\nEvidence: theory. Sources: source-9d15cd9236072f5c, source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-mathematical-assumptions-2\n\nThe model has a gap and a nonmagnetic singlet ground state, yet an isolated dimer has neither bulk topological order nor mobile charge. Adding a synthetic Curie contribution gives $\\chi_{\\mathrm{obs}}=\\chi_0+c/T$. With an illustrative gap of 6 K, c = 0.001 and T = 0.1 K, the background exceeds 99.9999% of the total response even though the intrinsic response is exponentially suppressed. The chosen 6 K is a model parameter, not the measured anomaly temperature or a fitted material gap. An inverse-temperature tail cannot by itself establish a gapless intrinsic state.\n\nEvidence: theory. Sources: source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-mathematical-assumptions-3\n\nFive finite-difference derivatives agree with the analytic response, and fifteen temperature/background combinations check this counterexample. Its Curie term assumes independent, unsaturated moments; interactions, anisotropy and finite-field saturation are excluded. Singlet correlations in an insulating model also do not demonstrate charge coherence or superconductivity. The separate [RVB discussion](/scwiki/rvb-and-doped-mott-insulators) examines wavefunction normalization and charge-response assumptions. These finite calculations are not a simulation of a bulk quantum spin liquid.\n\nEvidence: theory. Sources: source-5a6026d6455bf7a0, source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-experimental-criteria-1\n\nShimizu and colleagues' lowest-temperature proton NMR measurements used a single crystal at 2.2 T perpendicular to the conducting planes, reaching 32 mK. That temperature floor is not a zero-field result. Their higher-temperature polycrystalline NMR used 3.9 T, and susceptibility measurements used 0.32 T. No resolved splitting or major broadening was observed at low temperature, but the small-moment estimate relies on calibration against a different chloride salt. The absence of a resolved signal therefore has a probe- and model-dependent bound.\n\nEvidence: experiment. Sources: source-9d15cd9236072f5c.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-experimental-criteria-2\n\nBelow approximately 0.4 K, the reported recovery needs two exponential components, with roughly linear and quadratic temperature dependences of their relaxation rates. The authors discuss spatial inhomogeneity and possible disorder-related explanations. Combining these components into one universal power law would discard relevant evidence. The approximately 250 K exchange scale obtained from the susceptibility analysis is neither the 32 mK measurement floor nor a superconducting transition temperature.\n\nEvidence: experiment. Sources: source-9d15cd9236072f5c.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-experimental-criteria-3\n\nMiksch and colleagues separate a decreasing main ESR contribution below the approximately 6 K anomaly from narrow defect-related components. Their author manuscript uses conventional 9.5 GHz measurements near 340 mT down to 1.9 K, alongside separate low-frequency measurements near 40 mT reaching 25 mK. These are different protocols, not one continuous zero-field measurement. Samples from four laboratories show different defect signals. The proposed microscopic defect origin remains an interpretation; the final abstract describes a gapped ground state consistent with a valence-bond solid.\n\nEvidence: experiment. Sources: source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-limits-and-disputes-1\n\nGap values require their observable and fitting model. Miksch's author supplement compares a simple activated fit giving 7.3 K with a chain-based fit giving 12.1 K. Its main text and figure legend include an inverse-temperature prefactor that the displayed supplementary expression omits; no unreported correction or independent reproduction of that fit is claimed here. Pustogow's final paper explicitly distinguishes its transport scale $E_g=2\\Delta\\approx30$–50 K from the approximately 12 K ESR spin gap. These numbers are not interchangeable measurements of one quantity, nor evidence by themselves of a manuscript-version error.\n\nEvidence: hypothesis. Sources: source-5e0dcd80e8b64a1b, source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-limits-and-disputes-2\n\nThe strain-transport study favors a valence-bond-solid interpretation but leaves a gapped chiral spin liquid possible. Its hydrostatic-equivalent pressure is inferred for a substrate-coupled crystal; it is not a directly applied hydrostatic pressure. Kurosaki's pressure phase diagram establishes neighboring electronic phases and superconductivity, but proximity does not identify the pairing mediator. Complete scientific acceptance remains open: final-version comparisons, raw-data analysis, full calibration and discrimination among microscopic states are incomplete. Reference labels identify which selected methods, figures or abstracts were actually checked.\n\nEvidence: hypothesis. Sources: source-0443485ac20d3a8c, source-5e0dcd80e8b64a1b, source-ef796739e836bb78.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n### scwiki-g7-claim-discovery-implications-1\n\nRecord the sample, magnetic field, frequency or time window, temperature floor, background subtraction and fitting assumptions for each proposed spin-liquid signature. Compare magnetic, structural, thermodynamic and charge-coherence observations under compatible conditions. A useful mechanism proposal must predict observations that distinguish alternatives across the transition, including the behavior of defects. Superconductivity next to a candidate insulating state motivates such tests; it does not establish fractionalization-mediated pairing.\n\nEvidence: hypothesis. Sources: source-9d15cd9236072f5c, source-0443485ac20d3a8c, source-5e0dcd80e8b64a1b.\n\nConditions: Magnetic measurement windows and background models retained; transport and ESR gaps are distinct; independent finite dimer is not a material fit.\n\nVerification scope: Selected primary methods/figures and independent finite calculation; full scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-g7. Revision: ac215be3b2636cf6e38d. Updated: 2026-10-18T16:13:01.112201+00:00.\n\nReview scope: Selected Shimizu author methods/figures, Miksch author methods/supplement figure, Pustogow final passages and scoped historical abstracts; independent singlet-triplet/background checks.\n\n- Complete scientific acceptance remains open.\n- Full final-version comparison, raw-data reproduction and complete calibration remain incomplete.\n- A spin gap or missing magnetic order alone does not identify a quantum spin liquid.\n- The independent finite dimer/background is not a material fit or a bulk topological-state simulation.\n\nSource: [G_magnetism_interplay/G7_spin_liquid_SC.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/G_magnetism_interplay/G7_spin_liquid_SC.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 c290c1c28c6e96cc7734f29527752a2a352e46b552acfa7251562dbb9b84ae7f.\n","wordCount":893}}