Evolution of two-time correlations in dissipative quantum spin systems: aging and hierarchical dynamics

TL;DR

This paper investigates the evolution of two-time correlations in dissipative quantum spin systems, revealing aging and hierarchical dynamics through advanced simulation techniques and identifying three distinct dynamical regimes.

Contribution

It extends matrix product state methods to analyze two-time correlations in dissipative quantum systems, uncovering complex aging behaviors and dynamical regimes.

Findings

Identified three dynamical regimes: initial unitary, aging algebraic, and stretched exponential.

Demonstrated the dependence of correlation dynamics on interaction anisotropy.

Showed how dissipative heating can probe the Hamiltonian spectrum.

Abstract

We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For initial times, their evolution is dominated by the system unitary dynamics and depends on the initial state and the Hamiltonian parameters. For weak spin-spin interaction anisotropy, after this initial dynamical regime, two-time correlations enter an algebraic scaling regime signaling the breakdown of time-translation invariance and the emergence of aging. For stronger interaction anisotropy, these correlations first go through a stretched exponential regime before entering the algebraic one. Such complex relaxation arises due to the competition between the proliferation dynamics of energetically costly excitations and their motion. As a result, dissipative heating dynamics of spin systems can be used to probe the entire spectrum of the underlying Hamiltonian.