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

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.

5 pages, 3 figures + supplemental material (3 pages, 1 figure)

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• Dynamical scaling of correlations generated by short- and long-range dissipation
• Dynamical universality classes towards an infinite temperature state
• Comparing bipartite entropy growth in open-system matrix-product simulation methods
• Melting of the critical behavior of a Tomonaga-Luttinger liquid under dephasing
• Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence
• Relaxation of imbalance in a disordered XX model with on-site dephasing
• Non-unitarity maximizing unraveling of open quantum dynamics
• Transition between dissipatively stabilized helical states
• Interaction-impeded relaxation in the presence of finite temperature baths
• Dissipative Generation of Currents by Nonreciprocal Local and Global Environments