Nonequilibrium Steady State in a Quantum System: One-dimensional Transverse Ising Model with Energy Current

TL;DR

This paper investigates the nonequilibrium steady states of a one-dimensional transverse Ising model driven by an energy current, revealing a phase transition characterized by the emergence of power-law correlations and the destruction of magnetic order.

Contribution

It provides an exact analysis of the phase diagram and correlation functions in a quantum Ising chain under energy current, highlighting the transition to a current-carrying state.

Findings

Energy current appears above a critical field lambda_c(h).

Long-range order is destroyed in the current-carrying state.

Correlations exhibit power-law, oscillatory decay in the nonequilibrium state.

Abstract

We study the nonequilibrium steady states of an Ising chain in a transverse field, h, by investigating the effect of a field, lambda, which drives the current of energy. The zero-temperature, h-lambda phase diagram is determined exactly and it is found that the energy current appears continuously above a threshold, lambda > lambda_c(h). The long-range magnetic order (present for h<h_c, lambda < lambda_c) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.