$\mathcal{PT}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
Abstract
This work studies a -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 -unbroken phase, the system exhibits sustained oscillatory dynamics with suppressed decoherence, whereas in the -broken phase, additional dissipative channels accelerate decoherence and drive rapid convergence toward a stable steady state. These results shed light on how symmetry protects coherent light--matter interactions in non-Hermitian quantum systems.
Cite
@article{arxiv.2512.20277,
title = {$\mathcal{PT}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics},
author = {Yong-Xin Zhang and Qing-Hu Chen},
journal= {arXiv preprint arXiv:2512.20277},
year = {2025}
}