Entanglement entropy growth in stochastic conformal field theory and the KPZ class

TL;DR

This paper models a 1+1D conformal quantum field theory with stochastic noise, revealing KPZ class fluctuations in entanglement entropy growth, governed by Tracy-Widom distribution, thus extending KPZ universality to interacting quantum systems.

Contribution

It introduces a stochastic conformal field theory model that connects KPZ fluctuations to quantum entanglement dynamics, expanding the universality class to many-body quantum systems.

Findings

Entanglement entropy fluctuations follow Tracy-Widom distribution.

KPZ class fluctuations observed in a quantum field theory model.

Universal behavior extends to interacting many-body quantum systems.

Abstract

We introduce a model of effective conformal quantum field theory in dimension $d=1+1$ coupled to stochastic noise, where Kardar-Parisi-Zhang (KPZ) class fluctuations can be observed. The analysis of the quantum dynamics of the scaling operators reduces to the study of random trajectories in a random environment, modeled by Brownian vector fields. We use recent results on random walks in random environments to calculate the time-dependent entanglement entropy of a subsystem interval, starting from a factorized state. We find that the fluctuations of the entropy in the large deviation regime are governed by the universal Tracy-Widom distribution. This enlarges the KPZ class, previously observed in random circuit models, to a family of interacting many body quantum systems.