Oscillating-mode gap: an indicator of phase transition in open quantum many-body systems

TL;DR

This paper introduces the oscillating-mode gap as a new spectral indicator, alongside the Liouvillian gap, to better understand phase transitions in open quantum many-body systems, especially those involving oscillatory dynamics.

Contribution

It proposes the oscillating-mode gap as a novel spectral measure crucial for characterizing phases and transitions in open quantum systems, complementing the existing Liouvillian gap.

Findings

Both the Liouvillian gap and the oscillating-mode gap are necessary for complete phase characterization.

The oscillating-mode gap captures the decay of oscillatory modes not reflected by the Liouvillian gap.

Analysis of a dissipative boson system illustrates the importance of the oscillating-mode gap.

Abstract

It presents a significant challenge to elucidate the relationship between the phases of open quantum many-body systems and the spectral structure of their governing Liouvillian, which determines how the density matrix evolves. Previous studies have focused on the Liouvillian gap, defined as the decay rate of the most slowly-decaying mode, as a key indicator of dissipative phase transition, noting its closure in symmetry-broken phases and opening in disordered phases. In this work, we propose an additional spectral gap, termed the oscillating-mode gap, defined as the decay rate of the most slowly-decaying oscillating mode. Through the analysis of a prototype dissipative boson system, we demonstrate the necessity of both the Liouvillian gap and the oscillating-mode gap for the comprehensive characterization of the system's phases and the transitions between them.