Strange metal and superconductor in the two-dimensional Yukawa-Sachdev-Ye-Kitaev model

TL;DR

This paper numerically analyzes the 2d-YSYK model, revealing its potential to explain quantum phase transitions and superconductivity phenomena observed in cuprates, including spectral functions and superfluid stiffness behavior.

Contribution

It provides the first full numerical solutions of the 2d-YSYK model in both normal and superconducting states, connecting theoretical predictions with experimental cuprate observations.

Findings

Reproduces key features of cuprate spectral functions.

Shows increasing superfluid stiffness as critical temperature decreases.

Identifies a regime matching experimental cuprate behavior.

Abstract

The two-dimensional Yukawa-Sachdev-Ye-Kitaev (2d-YSYK) model provides a universal theory of quantum phase transitions in metals in the presence of quenched random spatial fluctuations in the local position of the quantum critical point. It has a Fermi surface coupled to a scalar field by spatially random Yukawa interactions. We present full numerical solutions of a self-consistent disorder averaged analysis of the 2d-YSYK model in both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Our results reproduce key aspects of observations in the cuprates as analyzed by Michon et al. (arXiv:2205.04030). We also find a regime of increasing zero temperature superfluid stiffness with decreasing superconducting critical temperature, as is observed in bulk cuprates.