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

TL;DR

This paper investigates a $ ext{PT}$-symmetric non-Hermitian spin--boson model with a continuous bosonic spectrum, revealing a single exceptional point and distinct dynamical behaviors compared to Hermitian systems, including oscillations and phase-dependent decoherence.

Contribution

It introduces a non-Hermitian spin--boson model with a continuous spectrum, analyzing its exceptional point structure and dynamical properties, highlighting differences from finite-mode models.

Findings

Only one exceptional point (EP) appears in the model.

Distinct dynamical signatures in $ ext{PT}$-unbroken and broken phases.

Oscillations with periodic amplified amplitude in the $ ext{PT}$-unbroken phase.

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.