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

• URL: http://arxiv.org/abs/2512.20277v1
• Date: Tue, 23 Dec 2025 11:31:00 GMT
• Title: $\mathcal{PT}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
• Abstract summary: This work studies a $mathcalPT$-symmetric non-Hermitian spin--boson model.<n>The time evolution of observables is investigated via the Dirac--Frenkel time-dependent variational principle.<n>Results shed light on how $mathcalPT$ symmetry protects coherent light-matter interactions in non-Hermitian quantum systems.
• Score: 2.631933359112648
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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