Spread of Entanglement in Non-Relativistic Theories

TL;DR

This paper investigates how entanglement spreads in non-relativistic quantum field theories after a quench, using holographic models to derive a linear response relation and a time-dependent first law of entanglement entropy.

Contribution

It introduces a simple holographic model for non-relativistic theories, deriving a linear response relation and a novel time-dependent first law of entanglement entropy.

Findings

Entanglement entropy of small subsystems follows a linear response relation.

A time-dependent first law of entanglement entropy is established.

Relative entropy-like term serves as an order parameter for out-of-equilibrium states.

Abstract

We use a simple holographic toy model to study global quantum quenches in strongly-coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our results in arxiv:1705.10324 , we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium-states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law and periodic.