Dissipative dynamics in isolated quantum spin chains after a local quench

TL;DR

This paper demonstrates that local quenches in isolated quantum spin chains lead to local relaxation resembling dissipation, driven by eigenstate thermalization, with integrability preventing this process, supported by numerical simulations in the thermodynamic limit.

Contribution

It shows that local quenches induce local relaxation in quantum spin chains via eigenstate thermalization, with numerical methods enabling long-time simulations.

Findings

Local quenches cause local relaxation in quantum spin chains.

Eigenstate thermalization underpins the observed dissipation.

Integrability inhibits local dissipation processes.

Abstract

We provide numerical evidence that after a local quench in an isolated infinite quantum spin chain, the quantum state locally relaxes to the ground state of the post-quenched Hamiltonian, i.e. dissipates. This is a consequence of the unitary quantum dynamics. A mechanism similar to the eigenstate thermalization hypothesis is shown to be responsible for the dissipation observed. We also demonstrate that integrability obstructs dissipation. The numerical simulations are done directly in the thermodynamic limit with a time-evolution algorithm based on matrix product states. The area law of entanglement entropy is observed to hold after the local quench. As a result, the simulations can be performed for long times with small bond dimensions. Various local quenches on the Ising chain and the three-state Potts chain are studied.