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

Abstract

We study the nonequilibrium steady states of an Ising chain in a transverse field $h$ by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature, $h$- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) 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.