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

TL;DR

This paper explores the phase diagram of the spin-1/2 Yukawa-SYK model, revealing how superconductivity preempts a quantum phase transition between non-Fermi liquid and insulator phases, with implications for understanding complex phase transitions.

Contribution

It demonstrates that in the Yukawa-SYK model, a pairing phase develops before the nFL-insulator transition, and maps the phase boundaries and critical points using analytic and Monte Carlo methods.

Findings

Superconducting phase preempts the nFL-insulator transition.

The superconducting critical temperature decreases rapidly beyond a certain chemical potential.

The phase diagram features a thermal critical point where nFL and insulator phases merge.

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.