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 h, which drives the current of energy. The zero-temperature, h-h 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.