Vaporization dynamics of a dissipative quantum liquid

TL;DR

This paper studies how a Luttinger liquid's quantum properties evolve when suddenly coupled to a dissipative environment, revealing fractionalization, exponential decay, and entropy growth, with potential experimental implications.

Contribution

It provides a detailed analysis of the non-equilibrium dynamics of a dissipative Luttinger liquid using Lindblad formalism and numerical simulations, highlighting new decay and entropy behaviors.

Findings

Fermionic excitations fractionalize with preserved power-law correlations.

Density matrix spectrum becomes gapped and collapses logarithmically over time.

Von Neumann entropy transitions from -t ln(t) to ln(t) growth regimes.

Abstract

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial non-integer power law exponents, accompanied by an exponential decay in time with interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as $-\ln(t)$. The von Neumann entropy crosses over from the early time $-t\ln(t)$ behaviour to $\ln(t)$ growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.