Exact solutions of interacting dissipative systems via weak symmetries

TL;DR

This paper introduces a method leveraging continuous weak symmetries to analytically diagonalize the Liouvillian of complex Markovian dissipative systems, enabling exact solutions for their dynamics and spectra.

Contribution

The authors develop a novel approach using weak symmetries to exactly solve the Liouvillian of strongly interacting dissipative quantum systems.

Findings

Successfully diagonalized Liouvillian for nonlinear bosonic systems

Computed full dissipation spectrum for inhomogeneous quantum Ising model

Method applicable to a broad class of driven-dissipative quantum systems

Abstract

We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method can be viewed as implementing an exact, sector-dependent mean-field decoupling, or alternatively, as a kind of quantum-to-classical mapping. We focus on two canonical examples: a nonlinear bosonic mode subject to incoherent loss and pumping, and an inhomogeneous quantum Ising model with arbitrary connectivity and local dissipation. In both cases, we calculate and analyze the full dissipation spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.