The Sachdev-Ye-Kitaev model and free Majorana variational states

TL;DR

This paper investigates how well free Majorana states can approximate the Sachdev-Ye-Kitaev model and its generalizations, revealing potential spin glass order and analyzing symmetry-breaking phases through analytic and numerical methods.

Contribution

It introduces a detailed analysis of free Majorana state approximations for the SYK model, including a generalization and exploration of symmetry-breaking phases.

Findings

Evidence of spin glass order in the generalized model

Inconclusive but suggestive results for spin glass order in the original SYK model at zero temperature

Insights into the properties of time-reversal symmetry breaking phases

Abstract

Through a mixture of analytic and numerical techniques, we explore the optimal approximation by a free Majorana state to individual disorder realizations of the Sachdev-Ye-Kitaev model, along with a generalization of it. We elucidate the properties of the known time-reversal symmetry breaking phase in the generalized model, finding strong evidence of "spin glass" order. For the Sachdev-Ye-Kitaev model itself, our results are inconclusive but suggest a similar order may be present at zero temperature.