Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor

Abstract

We analyze the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model, which describes complex fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. In a recent work [Phys. Rev. Research 2, 033084 (2020)] it has been shown that, upon varying filling or chemical potential, there exists a first-order quantum phase transition between a non-Fermi liquid (nFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be nFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on parameters the first-order quantum phase transition extend to finite-temperatures and terminate at a thermal critical point, beyond which the nFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide the model realization of the transition of nFL's towards superconductivity and insulating states, therefore offer a controlled platform for future investigations of the generic phase diagram that hosts nFL, insulator and superconductor and their phase transitions.

9 pages, 6 figures

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• Tunable non-Fermi liquid phase from coupling to two-level systems
• Solvable model for a charge-$4e$ superconductor
• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Quantum chaos and phase transition in the Yukawa-SYK model
• Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
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• Fractionalized Fermi liquids and the cuprate phase diagram
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• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants