Dynamical correlations in a dissipative XXZ spin chain

TL;DR

This paper investigates how dissipative processes affect dynamical spin correlations in the XXZ spin chain, revealing preserved universality classes at early times and exponential damping at long times.

Contribution

It introduces a comprehensive analysis of dynamical correlations in a dissipative XXZ chain, combining numerical and analytical methods to explore universality classes under Lindbladian dynamics.

Findings

Long-time correlations exhibit exponential damping.

Universality classes are preserved at early times.

Transverse correlations decay exponentially without wavefronts.

Abstract

We study dynamical spin correlations in a dissipative XXZ spin chain subject to uniform local spin-loss and pumping. Starting from a mixed steady state that is featureless albeit possessing finite magnetization, rich dynamics emerges in time-dependent two-point correlators evaluated on top of it. For unitary evolution in which the reservoir is absent, the longitudinal correlators reproduce the established hierarchy of spin-transport universality classes - ballistic, Kardar-Parisi-Zhang (KPZ) superdiffusive, and diffusive - across the phase diagram. However, for finite magnetization, additional ballistic light cone propagation gets superimposed on the previous universality classes, arising from magnon propagation.The transverse correlator displays very fast, exponential decay of correlations without wavefront propagation in the easy-plane case. At the isotropic point, it follows KPZ scaling due to $SU(2)$ symmetry, while in the easy-axis regime, it is characterized by ballistic spreading of correlations. Under full Lindbladian dynamics, the universality classes are preserved at early times, while the correlations acquire an overall exponential damping in the long-time limit. In terms of methods, we have used vectorized TEBD for numerical simulations and exact analytical results obtained via a Pfaffian representation and the third-quantization framework for the noninteracting XX case.