Transport and entanglement across integrable impurities from Generalized Hydrodynamics

TL;DR

This paper extends generalized hydrodynamics to include integrable quantum impurity models, enabling the study of non-equilibrium transport and entanglement in these systems with impurity scattering effects.

Contribution

The authors develop a Bethe-Boltzmann framework for impurity quantum impurity models within GHD, incorporating impurity scattering and entropy production, and analyze non-equilibrium dynamics.

Findings

Derived impurity GHD equations including entropy production

Analyzed bipartitioning quench with impurity effects

Obtained expressions for entanglement entropy and full counting statistics

Abstract

Quantum impurity models (QIMs) are ubiquitous throughout physics. As simplified toy models they provide crucial insights for understanding more complicated strongly correlated systems, while in their own right are accurate descriptions of many experimental platforms. In equilibrium, their physics is well understood and have proven a testing ground for many powerful theoretical tools, both numerical and analytical, in use today. Their non-equilibrium physics is much less studied and understood. However, the recent advancements in non equilibrium integrable quantum systems through the development of generalized hydrodynamics (GHD) coupled with the fact that many archetypal QIMs are in fact integrable presents an enticing opportunity to enhance our understanding of these systems. We take a step towards this by expanding the framework of GHD to incorporate integrable interacting QIMs. We present a set of Bethe-Boltzmann type equations which incorporate the effects of impurity scattering and discuss the new aspects which include entropy production. These impurity GHD equations are then used to study a bipartioning quench wherein a relevant backscattering impurity is included at the location of the bipartition. The density and current profiles are studied as a function of the impurity strength and expressions for the entanglement entropy and full counting statistics are derived.