Relaxation times of dissipative many-body quantum systems

TL;DR

This paper investigates how relaxation times in dissipative quantum many-body systems scale with system size, revealing phase transitions and differences between integrable and chaotic systems in their spectral gap behavior.

Contribution

It provides a detailed analysis of the spectral gap scaling and phase transitions in relaxation dynamics of quantum systems with boundary and bulk dissipation, highlighting new scaling regimes and bounds.

Findings

Different scaling regimes for bulk dissipation with a critical transition strength.

In boundary dissipation, the spectral gap is bounded by 1/L, with distinct scaling in integrable and chaotic systems.

Transition from exponential to algebraic gap in systems with localized modes.

Abstract

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than 1/L. In integrable systems with boundary dissipation one typically observes scaling 1/L^3, while in chaotic ones one can have faster relaxation with the gap scaling as 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.