Abstract
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 each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an 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 $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically 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.
Highlights
Many-body dynamics in closed quantum systems has exploded in popularity as an area of intense research over the last decade [1,2,3,4,5]
The work presented in this article focuses on the long-time behavior of one-body observables and correlation functions in the nonequilibrium steady state that forms in the center of the system as the domain-wall broadens, or “melts.” Previous efforts have demonstrated that the central subsystem relaxes to a generalized Gibbs ensemble (GGE)-like steady state when time evolution is generated by the isotropic [50] and anisotropic
Despite the presence of an energy gap in the spectrum of the Hamiltonian which generates time evolution, we find the persistence of power-law correlations in the spin-spin correlation functions
Summary
Many-body dynamics in closed quantum systems has exploded in popularity as an area of intense research over the last decade [1,2,3,4,5]. The work presented in this article focuses on the long-time behavior of one-body observables and correlation functions in the nonequilibrium steady state that forms in the center of the system as the domain-wall broadens, or “melts.” Previous efforts have demonstrated that the central subsystem relaxes to a GGE-like steady state when time evolution is generated by the isotropic [50] and anisotropic [46] XY models. In these cases, an effective momentum distribution describing the long-time limit of the central subsystem is obtained by expanding the initial momentum correlation matrix c†p+. IV contains a brief discussion and outlook on future work
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