Entanglement hamiltonian evolution during thermalization in conformal field theory

TL;DR

This paper investigates how the entanglement Hamiltonian evolves during thermalization in a (1+1)-D conformal field theory after a quantum quench, revealing that it converges to the thermal state over time.

Contribution

It provides exact forms of the entanglement Hamiltonian and spectrum during thermalization in a CFT, including the effects of generic initial states and modular flow analysis.

Findings

Entanglement Hamiltonian converges to thermal form at infinite time

Entanglement spectrum approaches steady state exponentially

Modular flows offer intuitive understanding of entanglement propagation

Abstract

In this work, we study the time evolution of the entanglement hamiltonian during the process of thermalization in a (1+1)-dimensional conformal field theory (CFT) after a quantum quench from a special class of initial states. In particular, we focus on a subsystem which is a finite interval at the end of a semi-infinite line. Based on conformal mappings, the exact forms of both entanglement hamiltonian and entanglement spectrum of the subsystem can be obtained. Aside from various interesting features, it is found that in the infinite time limit the entanglement hamiltonian and entanglement spectrum are exactly the same as those in the thermal ensemble. The entanglement spectrum approaches the steady state spectrum exponentially in time. We also study the modular flows generated by the entanglement hamiltonian in Minkowski spacetime, which provides us with an intuitive picture of how the entanglement propagates and how the subsystem is thermalized. Furthermore, the effect of a generic initial state is also discussed.