Bistabilities and domain walls in weakly open quantum systems

TL;DR

This paper investigates how weakly open quantum systems with approximate conservation laws can exhibit bistability and domain walls, analyzing the effects of noise and coupling strength through hydrodynamic models and numerical simulations.

Contribution

It introduces a hydrodynamic framework to describe domain wall formation and bistability in 1D quantum systems with approximate conservation laws under weak coupling.

Findings

Domain wall width scales as 1/√ε

Domain wall density is exponentially suppressed in 1/√ε

Hydrodynamic models accurately capture domain formation phenomena

Abstract

Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.