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

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.