Non-unitary dynamics of Sachdev-Ye-Kitaev chain

TL;DR

This paper explores non-unitary dynamics in a Sachdev-Ye-Kitaev chain, revealing phase transitions and critical regimes in entanglement behavior through path integral analysis.

Contribution

It introduces a novel non-unitary evolution framework for the SYK model and uncovers phase transitions and critical phenomena in entanglement dynamics.

Findings

First order phase transition from volume law to area law entanglement.

Emergence of a two-dimensional conformal symmetry in free fermion case.

Identification of a critical regime with extensive entanglement.

Abstract

We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.