# Quantum spin liquids and superconductivity: models and evidence

Compare solvable spin models with organic, kagome and Kitaev-material experiments, while separating candidate signatures, neutral excitations and charged superconducting order.

## Scope

A quantum spin liquid is a quantum magnetic state with correlations and excitations beyond a conventional ordered magnet. Absence of static magnetic order alone is not a definition that identifies it experimentally: a trivial singlet state, disorder or a finite measurement window can also suppress the expected signal. Candidate materials require positive evidence and tests of alternatives. Chiral spin liquids can break time-reversal symmetry, so preserving every conventional symmetry is not a universal requirement. [R1](#ref-source-779d3cdcbcd5a620) [R2](#ref-source-4619c72961e466c5) [R6](#ref-source-5e0dcd80e8b64a1b)

The connection to superconductivity is a research route, not an automatic consequence. Anderson's RVB proposal motivates doping a correlated singlet state, but undoped La2CuO4 has antiferromagnetic order. A spin-only Hamiltonian has no mobile electrical charge or superconducting stiffness. Emergent neutral Majorana fermions in such a model do not make its material a topological superconductor. A specific charge sector and gauge-invariant superconducting response must be established separately. [R1](#ref-source-779d3cdcbcd5a620) [R3](#ref-source-5a6026d6455bf7a0) [R11](#ref-source-9dda11fbf0c41f73) [R12](#ref-source-2f6a1c773323226a)

## Mathematical assumptions

An explicit counterexample clarifies the diagnostic problem. A product of disconnected spin singlets has $\langle\mathbf S_i\rangle=0$ and vanishing correlations between different dimers, yet is not thereby a long-range-entangled spin liquid. For two spin-one-half singlets, direct matrix evaluation gives $\langle\mathbf S_1\cdot\mathbf S_2\rangle=-3/4$ and $\langle\mathbf S_1\cdot\mathbf S_3\rangle=0$. These finite-state checks disprove the inference from zero local moments alone; they do not classify an interacting bulk material. [R2](#ref-source-4619c72961e466c5) [R6](#ref-source-5e0dcd80e8b64a1b)

Use the honeycomb convention $H=-\sum_{\langle ij\rangle_\alpha}J_\alpha\sigma_i^\alpha\sigma_j^\alpha$, with Pauli matrices $\sigma=2S$. A Hamiltonian written with spin operators requires couplings $K_\alpha=4J_\alpha$ for the same energy. The vortex-free zero-field matter spectrum has zeros when the three $|J_\alpha|$ satisfy triangle inequalities. Kitaev calls this the gapless B region, including isotropy; the dominant-coupling A regions are gapped. The source draft had these labels reversed. [R1](#ref-source-779d3cdcbcd5a620)

Near isotropy, a weak field with all three spin-axis components nonzero generates a time-reversal-breaking term scaling as $h_xh_yh_z/J^2$ at third order. This perturbative result is not exact solvability at arbitrary field. For an ideal equilibrated chiral Majorana edge above a gapped bulk, $\kappa_{xy}^{2D}/T=c_-\pi^2k_B^2/(3h)$ with $c_-=\pm1/2$. This is thermal conductance per layer, not three-dimensional conductivity or electrical Hall conductance. Independent checks verify the phase-boundary algebra, spin normalization and positive-energy thermal integral. [R1](#ref-source-779d3cdcbcd5a620)

For a gapped two-dimensional topologically ordered ground state and a sufficiently large smooth region, $S=\alpha L-\gamma+\cdots$ with $\gamma=\ln\mathcal D$ and $\mathcal D=\sqrt{\sum_a d_a^2}$. The Abelian Z2 example gives $\gamma=\ln2$. This expression is not a universal entropy formula for every gapless spin liquid, and a single entropy constant does not fully specify anyon statistics. Finite geometry, boundaries and correlation length matter before identifying a universal term. [R2](#ref-source-4619c72961e466c5)

## Experimental criteria

Shimizu's organic candidate kappa-(BEDT-TTF)2Cu2(CN)3 shows no proton-NMR signature of long-range magnetic order down to 32 mK. The single-crystal experiment applied 2.2 T perpendicular to the conducting planes; the susceptibility-derived exchange scale around 250 K came from a separate fit. Neither number is a superconducting transition temperature, and the experiment does not directly observe the zero-field, zero-temperature ground state. Kurosaki's pressure phase diagram separately connects the correlated insulator with metallic and superconducting regions; it does not identify a unique pairing mechanism. [R4](#ref-source-9d15cd9236072f5c) [R5](#ref-source-0443485ac20d3a8c)

Pustogow's 2023 strain-transport study instead favors a low-entropy, spin-gapped valence-bond-solid interpretation of the organic material's 6 K anomaly. Its hydrostatic-equivalent pressure is inferred from comparison with transport data, rather than directly applied hydrostatic pressure. The paper retains a gapped chiral-spin-liquid alternative and discusses mounting-related microcracks. Thus a revised interpretation must preserve both the measured anomaly and the remaining discrimination problem. [R6](#ref-source-5e0dcd80e8b64a1b)

Han's neutron study used deuterated herbertsmithite, ZnCu3(OD)6Cl2, at 1.6 K. Broad momentum-energy scattering supports the authors' fractionalization interpretation, but the measured low-energy signal can include interlayer Cu defects. The apparent absence of a gap down to the measured energy limit does not establish a universally gapless intrinsic kagome state. A later primary study explicitly analyzes correlated impurity contributions. Preserve isotope, background subtraction, resolution and momentum window before comparing these results with a theoretical continuum. [R7](#ref-source-43fba6076983bec0) [R8](#ref-source-7a6863ba09a1c037)

In alpha-RuCl3, zero-field magnetic order and candidate field-induced behavior must be separated. Xing's 2025 ultraclean-crystal study reports a narrower near-half-quantized thermal Hall plateau and weakened oscillation-like features. It discusses sample-dependent magnetic boundaries, possible stacking faults and phonon-edge coupling. The 5.0 K Hall measurement used heat current along b and field along a; the comparison crystal was measured at 4.3 K. These are not identical conditions or a universal material threshold. [R9](#ref-source-f089ec733f27462c)

Shragai's 2026 ultrasound study measures acoustic Faraday rotation and infers a phonon Hall-viscosity contribution. Its conversion to thermal transport requires assumptions about frequency, phonon branches and viscosity components; the directly measured single-component estimate does not independently measure every thermal carrier. One displayed comparison also combines 2 K, 55-degree-tilted ultrasound with 4.9 K, 45-degree-tilted thermal data. This supplies substantive phonon evidence without making every field geometry or claimed quantized plateau equivalent. [R10](#ref-source-4a3e383e4c71604e)

## Limits and disputes

A continuum, a low-temperature heat-capacity term, absent NMR splitting and a thermal Hall signal test different observables. Their interpretation depends on defects, phonons, magnetic order, probe time scales and sample history. Do not turn one positive signal into a sufficient spin-liquid criterion, or one disputed material interpretation into a claim about every possible quantum spin liquid. Broad statements that all materials are settled or that none can ever be established would exceed this review. [R4](#ref-source-9d15cd9236072f5c) [R6](#ref-source-5e0dcd80e8b64a1b) [R7](#ref-source-43fba6076983bec0) [R9](#ref-source-f089ec733f27462c) [R10](#ref-source-4a3e383e4c71604e)

Complete scientific acceptance remains open. The present check covers selected primary passages, figures and restricted independent models. Several references retain abstract-only or earlier manuscript scopes; complete final-version comparisons, defect subtraction, thermal calibration and raw-data reproduction remain unfinished. The exact-model results and experimental interpretations are therefore presented at different evidence levels. [R1](#ref-source-779d3cdcbcd5a620) [R2](#ref-source-4619c72961e466c5) [R4](#ref-source-9d15cd9236072f5c) [R5](#ref-source-0443485ac20d3a8c) [R7](#ref-source-43fba6076983bec0) [R8](#ref-source-7a6863ba09a1c037) [R9](#ref-source-f089ec733f27462c) [R10](#ref-source-4a3e383e4c71604e)

## Discovery implications

Track the insulating magnetic state, tuning parameter and superconducting response independently. For a pressure or doping trajectory, distinguish structural changes and disorder from changed bandwidth or filling. Compare several probes on characterized samples and ask what would exclude a trivial singlet, ordered or disordered alternative. A successful spin-liquid model provides testable mechanisms and excitations; establishing superconductivity additionally requires mobile charge, phase coherence and the corresponding experimental criteria. [R5](#ref-source-0443485ac20d3a8c) [R6](#ref-source-5e0dcd80e8b64a1b) [R11](#ref-source-9dda11fbf0c41f73) [R12](#ref-source-2f6a1c773323226a)

## Related topics

[Spin-liquid routes to superconductivity](/scwiki/spin-liquids-and-superconductivity), [RVB pairing](/scwiki/rvb-and-doped-mott-insulators), [Organic superconductors](/scwiki/organic-charge-transfer-superconductors), and [Mottness](/scwiki/mottness-and-superconductivity).

## Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.

| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |
|---|---|---|---|---|---|---|
| RuCl3 (aliases: alpha-RuCl3, RuCl3, ruthenium trichloride); Xing two-step-grown alpha-RuCl3 crystal; heat current b,field a | 5 K; 5K thermal Hall measurement temperature, not superconducting Tc or magnetic TN. | measurement; thermal-hall-measurement | Steady-state thermal transport | ambient; unknown GPa | unknown | experiment; [source](#ref-source-f089ec733f27462c) |

## Sources

### Ref source-779d3cdcbcd5a620

[R1] Anyons in an exactly solved model and beyond (2006). [DOI 10.1016/j.aop.2005.10.005](https://doi.org/10.1016/j.aop.2005.10.005). Publication: journal-article. Check: selected-final-phase-and-edge-check. Checked: 2026-10-19. Final PDFpp18–19(printed19–20) dispersion/phase labels,PDFp25(printed26) third-order field approximation andPDFpp27–28(printed28–29) Chern/edge passages read. PDFpp19/28 visually checked. B is gapless at isotropy; A regions gapped. Complete110-page argument not read. General field not claimed exactly solvable.
### Ref source-4619c72961e466c5

[R2] Topological Entanglement Entropy (2006). [DOI 10.1103/PhysRevLett.96.110404](https://doi.org/10.1103/PhysRevLett.96.110404). Publication: journal-article. Check: selected-author-entropy-equations. Checked: 2026-10-19. Authorv1,11October2005,pp1–2 read: gapped2D medium,large smooth region versus correlation length, gamma=log total quantum dimension, boundary-subtraction construction. Final comparison/full TQFT derivation not completed.
### Ref source-5a6026d6455bf7a0

[R3] 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.
### Ref source-9d15cd9236072f5c

[R4] 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-NMR-methods-and-spectra. Checked: 2026-10-19. Authorv1,19July2003; selected pp1–3 read;p2Figures2/3 andmethods visually checked. Single crystal76microgram,32mK–36K,2.2T perpendicular planes;polycrystal NMR3.9T; susceptibility0.32T. Exchange250K fromseries-fit susceptibility,notTc. No exactT=0/zero-field proof or final/raw audit.
### Ref source-0443485ac20d3a8c

[R5] 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.
### Ref source-5e0dcd80e8b64a1b

[R6] 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: 2026-10-18. 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.
### Ref source-43fba6076983bec0

[R7] Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet (2012). [DOI 10.1038/nature11659](https://doi.org/10.1038/nature11659). Publication: journal-article. Check: selected-author-neutron-methods-and-figure-check. Checked: 2026-10-19. Author upload18July2013 after2012journal. Selected pp2–6 read; p11Figures3/4 visually checked. Deuterated ZnCu3(OD)6Cl2 single crystal,MACS,1.6K; final energies5.1/3.0meV,resolution HWHM0.21/0.08meV. Low-energy interlayer impurities can mask intrinsic gap; no full background/raw-data audit.
### Ref source-7a6863ba09a1c037

[R8] Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite (2016). [DOI 10.1103/PhysRevB.94.060409](https://doi.org/10.1103/PhysRevB.94.060409). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-19. Original abstract checked: low-energy interlayer impurity correlations in deuterated herbertsmithite. Full neutron decomposition not reviewed; no new exact intrinsic gap extracted.
### Ref source-f089ec733f27462c

[R9] Magnetothermal transport in ultraclean single crystals of Kitaev magnet alpha-RuCl3 (2025). [DOI 10.1038/s41535-025-00749-4](https://doi.org/10.1038/s41535-025-00749-4). Publication: journal-article. Check: selected-author-transport-results-and-methods. Checked: 2026-10-19. Authorv2,29March2025; publisher28March2025. Selected HTML results,Figure4caption andmethods read: q||b,fieldalong a,5.0Ksample versus4.3Kcomparison,plateau narrower,steady-state transport,two-stepCVT/sublimation. Same-sample orthogonal transport still desired. No Figure4visual/raw-data audit; rendering date notpublication.
### Ref source-4a3e383e4c71604e

[R10] Phonon Hall viscosity and the intrinsic thermal Hall effect of alpha-RuCl3 (2026). [DOI 10.1038/s41586-026-10420-y](https://doi.org/10.1038/s41586-026-10420-y). Publication: journal-article. Check: selected-author-ultrasound-and-comparison-check. Checked: 2026-10-19. Authorv2,9May2026; Nature652,1166–1172. Selected pp5–7,9–13 read;p12visually checked.2K ultrasound B||c and55degree tilt; frequency-dependent viscosity; single-branch estimate withinfactor6, otherbranches/tensor terms inferred. Figure5b compares2K55degree ultrasound with4.9K45degree literature Hall. Full final/supplement/calibration comparison remains open.
### Ref source-9dda11fbf0c41f73

[R11] Antiferromagnetism in La2CuO4-y (1987). [DOI 10.1103/PhysRevLett.58.2802](https://doi.org/10.1103/PhysRevLett.58.2802). Publication: journal-article. Check: publisher-abstract-scoped-check. Checked: 2026-10-18. Powder neutron magnetic superlattice evidence for antiferromagnetism in undoped parent. Abstract only; full refinement not checked.
### Ref source-2f6a1c773323226a

[R12] Doping a Mott insulator: Physics of high-temperature superconductivity (2006). [DOI 10.1103/RevModPhys.78.17](https://doi.org/10.1103/RevModPhys.78.17). Publication: journal-article. Check: earlier-author-manuscript-selected-passages-check. Checked: 2026-10-18. Selected manuscript pp.27–28 projected Hilbert space and constraint, p.33 Gaussian response and experimental mismatch, p.45 representation versus emergent gauge group. Page33 equations visually inspected. Full final-version comparison pending.

## Claim evidence and conditions

### scwiki-h10-claim-scope-1

A quantum spin liquid is a quantum magnetic state with correlations and excitations beyond a conventional ordered magnet. Absence of static magnetic order alone is not a definition that identifies it experimentally: a trivial singlet state, disorder or a finite measurement window can also suppress the expected signal. Candidate materials require positive evidence and tests of alternatives. Chiral spin liquids can break time-reversal symmetry, so preserving every conventional symmetry is not a universal requirement.

Evidence: hypothesis. Sources: source-779d3cdcbcd5a620, source-4619c72961e466c5, source-5e0dcd80e8b64a1b.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-scope-2

The connection to superconductivity is a research route, not an automatic consequence. Anderson's RVB proposal motivates doping a correlated singlet state, but undoped La2CuO4 has antiferromagnetic order. A spin-only Hamiltonian has no mobile electrical charge or superconducting stiffness. Emergent neutral Majorana fermions in such a model do not make its material a topological superconductor. A specific charge sector and gauge-invariant superconducting response must be established separately.

Evidence: hypothesis. Sources: source-779d3cdcbcd5a620, source-5a6026d6455bf7a0, source-9dda11fbf0c41f73, source-2f6a1c773323226a.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-mathematical-assumptions-1

An explicit counterexample clarifies the diagnostic problem. A product of disconnected spin singlets has $\langle\mathbf S_i\rangle=0$ and vanishing correlations between different dimers, yet is not thereby a long-range-entangled spin liquid. For two spin-one-half singlets, direct matrix evaluation gives $\langle\mathbf S_1\cdot\mathbf S_2\rangle=-3/4$ and $\langle\mathbf S_1\cdot\mathbf S_3\rangle=0$. These finite-state checks disprove the inference from zero local moments alone; they do not classify an interacting bulk material.

Evidence: theory. Sources: source-4619c72961e466c5, source-5e0dcd80e8b64a1b.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-mathematical-assumptions-2

Use the honeycomb convention $H=-\sum_{\langle ij\rangle_\alpha}J_\alpha\sigma_i^\alpha\sigma_j^\alpha$, with Pauli matrices $\sigma=2S$. A Hamiltonian written with spin operators requires couplings $K_\alpha=4J_\alpha$ for the same energy. The vortex-free zero-field matter spectrum has zeros when the three $|J_\alpha|$ satisfy triangle inequalities. Kitaev calls this the gapless B region, including isotropy; the dominant-coupling A regions are gapped. The source draft had these labels reversed.

Evidence: theory. Sources: source-779d3cdcbcd5a620.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-mathematical-assumptions-3

Near isotropy, a weak field with all three spin-axis components nonzero generates a time-reversal-breaking term scaling as $h_xh_yh_z/J^2$ at third order. This perturbative result is not exact solvability at arbitrary field. For an ideal equilibrated chiral Majorana edge above a gapped bulk, $\kappa_{xy}^{2D}/T=c_-\pi^2k_B^2/(3h)$ with $c_-=\pm1/2$. This is thermal conductance per layer, not three-dimensional conductivity or electrical Hall conductance. Independent checks verify the phase-boundary algebra, spin normalization and positive-energy thermal integral.

Evidence: theory. Sources: source-779d3cdcbcd5a620.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-mathematical-assumptions-4

For a gapped two-dimensional topologically ordered ground state and a sufficiently large smooth region, $S=\alpha L-\gamma+\cdots$ with $\gamma=\ln\mathcal D$ and $\mathcal D=\sqrt{\sum_a d_a^2}$. The Abelian Z2 example gives $\gamma=\ln2$. This expression is not a universal entropy formula for every gapless spin liquid, and a single entropy constant does not fully specify anyon statistics. Finite geometry, boundaries and correlation length matter before identifying a universal term.

Evidence: theory. Sources: source-4619c72961e466c5.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-experimental-criteria-1

Shimizu's organic candidate kappa-(BEDT-TTF)2Cu2(CN)3 shows no proton-NMR signature of long-range magnetic order down to 32 mK. The single-crystal experiment applied 2.2 T perpendicular to the conducting planes; the susceptibility-derived exchange scale around 250 K came from a separate fit. Neither number is a superconducting transition temperature, and the experiment does not directly observe the zero-field, zero-temperature ground state. Kurosaki's pressure phase diagram separately connects the correlated insulator with metallic and superconducting regions; it does not identify a unique pairing mechanism.

Evidence: experiment. Sources: source-9d15cd9236072f5c, source-0443485ac20d3a8c.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-experimental-criteria-2

Pustogow's 2023 strain-transport study instead favors a low-entropy, spin-gapped valence-bond-solid interpretation of the organic material's 6 K anomaly. Its hydrostatic-equivalent pressure is inferred from comparison with transport data, rather than directly applied hydrostatic pressure. The paper retains a gapped chiral-spin-liquid alternative and discusses mounting-related microcracks. Thus a revised interpretation must preserve both the measured anomaly and the remaining discrimination problem.

Evidence: experiment. Sources: source-5e0dcd80e8b64a1b.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-experimental-criteria-3

Han's neutron study used deuterated herbertsmithite, ZnCu3(OD)6Cl2, at 1.6 K. Broad momentum-energy scattering supports the authors' fractionalization interpretation, but the measured low-energy signal can include interlayer Cu defects. The apparent absence of a gap down to the measured energy limit does not establish a universally gapless intrinsic kagome state. A later primary study explicitly analyzes correlated impurity contributions. Preserve isotope, background subtraction, resolution and momentum window before comparing these results with a theoretical continuum.

Evidence: experiment. Sources: source-43fba6076983bec0, source-7a6863ba09a1c037.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-experimental-criteria-4

In alpha-RuCl3, zero-field magnetic order and candidate field-induced behavior must be separated. Xing's 2025 ultraclean-crystal study reports a narrower near-half-quantized thermal Hall plateau and weakened oscillation-like features. It discusses sample-dependent magnetic boundaries, possible stacking faults and phonon-edge coupling. The 5.0 K Hall measurement used heat current along b and field along a; the comparison crystal was measured at 4.3 K. These are not identical conditions or a universal material threshold.

Evidence: experiment. Sources: source-f089ec733f27462c.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-experimental-criteria-5

Shragai's 2026 ultrasound study measures acoustic Faraday rotation and infers a phonon Hall-viscosity contribution. Its conversion to thermal transport requires assumptions about frequency, phonon branches and viscosity components; the directly measured single-component estimate does not independently measure every thermal carrier. One displayed comparison also combines 2 K, 55-degree-tilted ultrasound with 4.9 K, 45-degree-tilted thermal data. This supplies substantive phonon evidence without making every field geometry or claimed quantized plateau equivalent.

Evidence: experiment. Sources: source-4a3e383e4c71604e.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-limits-and-disputes-1

A continuum, a low-temperature heat-capacity term, absent NMR splitting and a thermal Hall signal test different observables. Their interpretation depends on defects, phonons, magnetic order, probe time scales and sample history. Do not turn one positive signal into a sufficient spin-liquid criterion, or one disputed material interpretation into a claim about every possible quantum spin liquid. Broad statements that all materials are settled or that none can ever be established would exceed this review.

Evidence: hypothesis. Sources: source-9d15cd9236072f5c, source-5e0dcd80e8b64a1b, source-43fba6076983bec0, source-f089ec733f27462c, source-4a3e383e4c71604e.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-limits-and-disputes-2

Complete scientific acceptance remains open. The present check covers selected primary passages, figures and restricted independent models. Several references retain abstract-only or earlier manuscript scopes; complete final-version comparisons, defect subtraction, thermal calibration and raw-data reproduction remain unfinished. The exact-model results and experimental interpretations are therefore presented at different evidence levels.

Evidence: hypothesis. Sources: source-779d3cdcbcd5a620, source-4619c72961e466c5, source-9d15cd9236072f5c, source-0443485ac20d3a8c, source-43fba6076983bec0, source-7a6863ba09a1c037, source-f089ec733f27462c, source-4a3e383e4c71604e.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

### scwiki-h10-claim-discovery-implications-1

Track the insulating magnetic state, tuning parameter and superconducting response independently. For a pressure or doping trajectory, distinguish structural changes and disorder from changed bandwidth or filling. Compare several probes on characterized samples and ask what would exclude a trivial singlet, ordered or disordered alternative. A successful spin-liquid model provides testable mechanisms and excitations; establishing superconductivity additionally requires mobile charge, phase coherence and the corresponding experimental criteria.

Evidence: hypothesis. Sources: source-0443485ac20d3a8c, source-5e0dcd80e8b64a1b, source-9dda11fbf0c41f73, source-2f6a1c773323226a.

Conditions: Distinguish exact spin model, restricted illustrations and material interpretations. Preserve field, temperature, isotope, normalizations, defects and charge-sector criteria.

Verification scope: Selected primary text/figures and independent model checks; full scientific acceptance remains open.

## Revision and review

Article ID: scwiki-h10. Revision: 5e8fe8acc078f78e51af. Updated: 2026-10-18T17:32:52.513035+00:00.

Review scope: Kitaev final selected phase/edge passages, Kitaev-Preskill author entropy equations, Shimizu NMR methods/figures, Han neutron methods/figures, Xing selected transport results/methods and Shragai selected ultrasound comparisons; inherited B9 scopes.

- Complete scientific acceptance remains open.
- Complete primary final-version/supplement/raw-data, disorder and thermal-calibration audits remain open.
- Kurosaki,Anderson,Vaknin and Han2016 retain abstract-level limits.
- Independent models do not establish a material ground state, full topological classification or superconductivity.

Source: [H_anomalous_normal_state/H10_spin_liquid.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/H_anomalous_normal_state/H10_spin_liquid.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 27bd58e1a03a8a66f696e36ddafe920be685805b75e96b260aa585e231c725c8.