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Non-Hermitian Bethe-Salpeter Equation for Open Systems: Emergence of Exceptional Points in Excitonic Spectra from First Principles

Zhenlin Zhang1, Wei Hu1, Enrico Perfetto2,3, and Gianluca Stefanucci2,3

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Phys. Rev. X 16, 031020 – Published 28 July, 2026

DOI: https://doi.org/10.1103/4488-tqfp

Abstract

In open quantum systems hosting excitons, dissipation mechanisms critically shape the excitonic dynamics, band structure, and topological properties. A microscopic understanding of excitons in such non-Hermitian settings demands a first-principles generalization of the Bethe-Salpeter equation (BSE). Building on a recently introduced nonequilibrium Green’s function formalism compatible with Lindbladian dynamics, we derive a non-Hermitian BSE from diagrammatic perturbation theory on the Keldysh contour, and obtain a microscopic excitonic Hamiltonian that incorporates dissipation while preserving causality. We apply the formalism to valley excitons in transition metal dichalcogenides coupled to structured photon baths. We uncover a rich landscape of exceptional points in momentum space, forming either discrete sets or continuous manifolds, depending on bath structure. The exceptional points give rise to nonanalytic valley polarization, unusual polarization pattern in photoluminescence, and nontrivial topological signatures. Our results establish a first-principles framework for predicting and controlling excitonic behavior in open quantum materials, showing how engineered environments can be leveraged to induce and manipulate non-Hermitian and topological properties.

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Modeling exciton behavior in open quantum systems remains a major theoretical challenge because conventional frameworks cannot capture the continuous flow of energy between a material and the external environment. We addressed this by developing a first-principles framework that extends the Bethe-Salpeter equation to incorporate the effects of dissipation and decoherence while preserving the causal structure of quantum dynamics. Applying this formalism to valley excitons in transition metal dichalcogenides, we demonstrated that engineered photonic environments can induce a rich landscape of exceptional points where distinct quantum states merge into one. Our calculations show that these spectral singularities lead to striking observable phenomena, including nonanalytic valley polarization and unusual light emission patterns. These results provide a predictive tool for controlling the optical and valleytronic properties of open quantum structures. Our work establishes a rigorous foundation for designing non-Hermitian quantum devices that leverage environmental coupling to manipulate excitonic states.

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Phys. Rev. X 16, 031020– Published 28 July, 2026
  • Received 15 October 2025
  • Revised 20 March 2026
  • Accepted 27 May 2026
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