Dissipative dynamics in the free massive boson limit of the sine-Gordon model

TL;DR

This paper investigates the dissipative dynamics of a one-dimensional sine-Gordon model in its free massive boson limit, revealing how correlations, order parameters, and entropy evolve under environmental coupling.

Contribution

It provides a detailed analysis of how dissipation affects correlations, order parameters, and entropy growth in the sine-Gordon model's free massive boson limit, incorporating forward scattering processes.

Findings

Single particle density matrix decays exponentially over time.

Charge density wave order parameter decays exponentially, independent of interactions.

Second Rénnyi entropy grows linearly with time, unaffected by the gap.

Abstract

We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to $-\gamma t|x|\Delta^2$ where $\gamma$ and $\Delta$ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R\'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.