Volume 131, Number 1, July 2020
|Number of page(s)||7|
|Published online||05 August 2020|
Entanglement entropy growth in stochastic conformal field theory and the KPZ class
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris - 75005 Paris, France
Received: 22 May 2020
Accepted: 30 June 2020
We introduce a model of effective conformal quantum field theory in dimension 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.
PACS: 05.30.-d – Quantum statistical mechanics / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
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