Replica Symmetry Breaking and Phase Transitions in a PT Symmetric Sachdev-Ye-Kitaev Model

TL;DR

This paper investigates the low temperature phases of PT symmetric Sachdev-Ye-Kitaev models and similar non-Hermitian systems, revealing replica symmetry breaking, phase transitions, and connections to gravitational wormholes.

Contribution

It demonstrates replica symmetry breaking and phase transition phenomena in PT symmetric SYK models, linking quantum chaos, non-Hermitian physics, and gravity analogies.

Findings

Replica symmetry breaking dominates low temperature phases.

Spectrum of the replica theory has a gap in the SYK model.

Non-chaotic SYK exhibits gapless spectrum and multiple second order transitions.

Abstract

We show that the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices are dominated by replica symmetry breaking configurations with a nearly flat free energy that terminates in a first order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relation between both configurations. For a non-chaotic SYK, the results are qualitatively different: the spectrum is gapless in the low temperature phase and there is an infinite number of second order phase transitions unrelated to the restoration of replica symmetry.