Poor man's approach to thermalization in Luttinger liquid

TL;DR

This paper investigates the non-equilibrium thermalization process of a Luttinger liquid after quantum and dissipative quenches, revealing universal entropy behavior and diverse dynamical regimes through bosonization.

Contribution

It introduces a simple approach to study thermalization in Luttinger liquids under Lindblad dynamics, highlighting universal entropy evolution and complex phase diagram features.

Findings

Entropy exhibits maxima, minima, or monotonic growth before thermalization.

Rich spatio-temporal behaviors include thermal, prethermal, and dissipation-enhanced regimes.

Dissipation can induce Fermi liquid-like responses in the system.

Abstract

We study the non-equilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density matrix reveals rich behaviour in the spatio-temporal "phase diagram", including thermal, prethermal and dissipation enhanced sudden quench Luttinger liquid behaviour as well as dissipation enhanced Fermi liquid response.