Graph symmetry organizes exceptional dynamics in open quantum systems

Abstract

Exceptional points (EPs) play a central role in non-Hermitian physics, yet most theoretical studies begin from deliberately engineered low-dimensional effective Hamiltonians whose parameters are tuned to produce spectral degeneracies. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and generally not amenable to a priori reduction. A general framework for identifying exceptional dynamics directly from microscopic dissipative models has therefore been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. We show that correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, from which the minimal non-Hermitian generators governing exceptional dynamics emerge naturally and exactly. We further introduce a numerical diagnostic–the exceptional-point strength, $$\mathcal {E}$$ –based on eigenvector conditioning, which quantifies proximity to defective Liouvillian 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 second-order exceptional points. More broadly, the framework establishes graph symmetry as a constructive principle for uncovering exceptional dynamics directly from microscopic Lindblad models, providing a scalable route to identifying hidden defective structure in complex open quantum systems.