Thermalization of entanglement

TL;DR

This paper investigates how entanglement entropy in quantum-chaotic spin chains relaxes to equilibrium, revealing slow relaxation linked to energy transport in Hamiltonian systems, unlike in Floquet systems without conserved energy.

Contribution

It demonstrates the role of energy conservation in slow entanglement relaxation and compares dynamics between Hamiltonian and Floquet spin chains.

Findings

Slow relaxation of entanglement entropy near equilibrium in Hamiltonian systems.

Absence of slow relaxation in Floquet systems without energy conservation.

Slow diffusive energy transport underpins the entanglement relaxation process.

Abstract

We explore the dynamics of the entanglement entropy near equilibrium in highly-entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.