Graph Symmetry Organizes Exceptional Dynamics in Open Quantum Systems

TL;DR

This paper develops a symmetry-based framework to identify and analyze exceptional points in the spectral structure of open quantum systems directly from microscopic models, enabling scalable analysis of complex dissipative dynamics.

Contribution

It introduces a symmetry-resolved approach and a numerical diagnostic for detecting exceptional points directly from the full Liouvillian, applicable to high-dimensional open quantum systems.

Findings

Reproduces analytically predicted exceptional seams in models

Reveals universal scaling of exceptional-point strength near EPs

Enables systematic discovery of hidden exceptional structures

Abstract

Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit exceptional behavior. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and not obviously reducible to minimal non-Hermitian models. A general framework for discovering exceptional dynamics directly from microscopic dissipative models has been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. Correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, within which minimal non-Hermitian blocks govern the onset of EPs and PT-breaking behavior. We further introduce a numerical diagnostic - the exceptional-point strength $\mathcal{E}$ - based on eigenvector conditioning, which quantifies proximity to defective dynamics without requiring analytic reduction. Applied to tight-binding models with correlated dephasing and relaxation, the method reproduces analytically predicted exceptional seams and reveals universal scaling of $\mathcal{E}$ near EP manifolds. More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems and is naturally compatible with matrix-free and tensor-network implementations for scalable many-body applications.