Dissipation induced Luttinger liquid correlations in a one dimensional Fermi gas

TL;DR

This paper investigates how dissipation affects a one-dimensional Fermi gas, revealing that dissipation induces Luttinger liquid correlations and alters information spreading and entropy growth.

Contribution

It demonstrates that dissipation leads to Luttinger liquid behavior in a Fermi gas, with unique decay laws and modified information velocity, expanding understanding of open quantum systems.

Findings

Dissipation causes a transition to Luttinger liquid correlations.

The information spreading velocity is set by dissipation, not excitation propagation.

Entropy initially grows as -t ln t and saturates to an extensive value.

Abstract

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a non-integer power law decay for late times, representing dissipation induced Luttinger liquid behaviour. However, the crossover between the two regions occurs due to dissipation induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as $-t\ln t$ initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.