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

## TL;DR

This paper demonstrates that power-law correlations persist in nonequilibrium steady states of gapped quantum spin chains, despite the exponential decay of ground-state correlations, by analyzing driven $XY$ models with energy gaps.

## Contribution

It shows that quasi-long range order exists in nonequilibrium steady states of gapped $XY$ spin chains, extending understanding of correlation behaviors beyond ground states.

## Key findings

- Power-law correlations persist in nonequilibrium steady states.
- Exponential decay of ground-state correlations does not imply decay in nonequilibrium.
- Analytical results obtained for magnetization, spin current, and correlations.

## 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.