Sachdev-Ye-Kitaev superconductivity: Quantum Kuramoto and generalized Richardson models

Hanteng Wang; A. L. Chudnovskiy; Alexander Gorsky; Alex Kamenev

doi:10.1103/PhysRevResearch.2.033025

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Sachdev-Ye-Kitaev superconductivity: Quantum Kuramoto and generalized Richardson models

Hanteng Wang, A. L. Chudnovskiy, Alexander Gorsky, Alex Kamenev

DOI 10.1103/PhysRevResearch.2.033025 · Physical Review Research

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Abstract

The Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of non-Fermi-liquid behavior. Here we investigate a possibility of having a superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase within the SYK framework. We found that ODLRO may be established in a spin-1/2 version of the model with the time-reversal invariance and an extra attractive interaction. If the latter is taken as the on-site negative U Hubbard term, it leads to the pseudogap phase at U<Uc dominated by quantum fluctuations of local phases. These fluctuations are described by a quantum version of the Kuramoto model, traditionally employed to illustrate synchronization of classical nonlinear oscillators. In the opposite limit of large U, the SYK + Hubbard model is approaching a certain generalization of the integrable Richardson model. We present exact diagonalization studies, along with analytic solutions of the aforementioned limiting cases. We also discuss possible holographic interpretations of the model, ODLRO, and the pseudogap.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
SYK+Hubbard Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown