Nonequilibrium Steady States in the Weakly-Coupled XXZ Model

TL;DR

This paper investigates nonequilibrium steady states in the weakly-coupled XXZ spin chain model, revealing a projection operator-based density matrix approximation and deriving an exact solution in a specific limit.

Contribution

It introduces a projection operator representation for the density matrix in NESS of the XXZ model and provides an analytical solution as q approaches zero.

Findings

Numerical calculations of temperature profiles, energy currents, and correlations for large spin chains.

Approximate density matrix expressed using quantum group $U_q(sl_2)$ projection operators.

Exact density matrix derived analytically in the limit $q ightarrow 0$.

Abstract

We study nonequilibrium steady states (NESSs) in the weakly-coupled XXZ model in contact with two heat baths at different temperatures. We show that the density matrix can be represented using only projection operators specified by the quantum numbers of the quantum group $U_q(sl_2)$ in a very good approximation. By using this property, we numerically calculate physical quantities such as temperature profile, energy current, and correlation functions, for the spin chain consisting of several hundred spins. We analytically derive the exact density matrix in the limit $q \rightarrow 0$.