Dynamical transitions from slow to fast relaxation in random open quantum systems

TL;DR

This paper investigates how spatial locality influences the relaxation dynamics of random open quantum systems, revealing phase transitions in relaxation behavior depending on decay exponents and noise strength.

Contribution

It introduces a model with power-law decaying interactions in quantum systems under noise, analyzing phase transitions in relaxation dynamics and identifying nonperturbative effects.

Findings

Three distinct relaxation phases depending on decay exponents.

Existence of phase transitions as a function of noise strength.

Nonperturbative effects prevent phase transitions in the thermodynamic limit.

Abstract

We explore the effects of spatial locality on the dynamics of random quantum systems subject to a Markovian noise. To this end, we study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose entries decay as power laws of distance, with distinct exponents $\alpha_H, \alpha_L$. The steady state is always featureless, but the rate at which it is approached exhibits three phases depending on $\alpha_H$ and $\alpha_L$: a phase where the approach is asymptotically exponential as a result of a gap in the spectrum of the Lindblad superoperator that generates the dynamics, and two gapless phases with subexponential relaxation, distinguished by the manner in which the gap decreases with system size. Within perturbation theory, the phase boundaries in the $(\alpha_H, \alpha_L)$ plane differ for weak and strong dissipation, suggesting phase transitions as a function of noise strength. We identify nonperturbative effects that prevent such phase transitions in the thermodynamic limit.