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arXiv:2512.20277 · Physical Review A

$\mathcal{PT}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics

Yong-Xin Zhang, Qing-Hu Chen

quant-phSubmitted Dec 23, 2025• Announced Dec 24, 2025• 0 citations• Revised Jun 16, 2026 (v2)
v1 · Dec 23, 2025v2 · Jun 16, 2026
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Abstract

This work studies a $\mathcal{PT}$-symmetric non-Hermitian spin--boson model, consisting of a non-Hermitian two-level system coupled to a continuous bosonic bath. The static properties of the system are analyzed through a projection method derived from the displacement operator. We find that only a single exceptional point (EP) emerges, in contrast to non-Hermitian spin--boson models with finite modes, which typically exhibit multiple EPs. Notably, only a single real eigenvalue is found before the EP, which differs markedly from typical non-Hermitian systems where a pair of real eigenvalues precedes the EP. The time evolution of observables is further investigated via the Dirac--Frenkel time-dependent variational principle. Compared to its Hermitian counterpart, the non-Hermitian model exhibits distinct dynamical signatures, most notably the emergence of oscillations with periodic amplified amplitude. In the $\mathcal{PT}$-unbroken phase, the system exhibits sustained oscillatory dynamics with suppressed decoherence, whereas in the $\mathcal{PT}$-broken phase, additional dissipative channels accelerate decoherence and drive rapid convergence toward a stable steady state. These results shed light on how $\mathcal{PT}$ symmetry protects coherent light--matter interactions in non-Hermitian quantum systems.

Journal reference
Phys.Rev.A 113,063723(2026)
DOI
10.1103/7ydc-81gz

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This work studies a PT\mathcal{PT}PT-symmetric non-Hermitian spin--boson model, consisting of a non-Hermitian two-level system coupled to a continuous bosonic bath. The static properties of the system are analyzed through a projection method derived from the displacement operator. We find that only a single exceptional point (EP) emerges, in contrast to non-Hermitian spin--boson models with finite modes, which typically exhibit multiple EPs. Notably, only a single real eigenvalue is found before the EP, which differs markedly from typical non-Hermitian systems where a pair of real eigenvalues precedes the EP. The time evolution of observables is further investigated via the Dirac--Frenkel time-dependent variational principle. Compared to its Hermitian counterpart, the non-Hermitian model exhibits distinct dynamical signatures, most notably the emergence of oscillations with periodic amplified amplitude. In the PT\mathcal{PT}PT-unbroken phase, the system exhibits sustained oscillatory dynamics with suppressed decoherence, whereas in the PT\mathcal{PT}PT-broken phase, additional dissipative channels accelerate decoherence and drive rapid convergence toward a stable steady state. These results shed light on how PT\mathcal{PT}PT symmetry protects coherent light--matter interactions in non-Hermitian quantum systems.
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