Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

TL;DR

This paper uncovers an emergent conformal symmetry in non-Hermitian SYK$_2$ chains, explaining critical phases with power-law correlations and logarithmic entanglement through a solvable theoretical framework.

Contribution

It introduces a solvable model of non-Hermitian SYK$_2$ chains revealing emergent conformal symmetry and critical behavior of correlations and entanglement.

Findings

Emergent conformal field theory of Goldstone modes

Universal critical behavior of squared correlators

Logarithmic entanglement entropy proportional to subsystem size

Abstract

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem ${A}$ with length ${L_A}$ corresponds to the energy of the half-vortex pair ${S\sim \rho_s \log L_A}$, where ${\rho_s}$ is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.