Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains

The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic XY spin chains including of two types of additional terms that generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the transverse direction or introducing a modulation to the XY coupling. The magnetization, spin current and spin-spin correlation functions are computed in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground state correlation functions exhibiting exponential decay. It is discussed how these power-law correlations appear related to the periodic nature of the perturbation which generates the energy gap.