Dissipation effects of an anharmonic environment on the Spin-Boson model

Complex quantum systems are often described as a small subsystem coupled to a large environment, leading to energy exchange and dissipation. In solid-state platforms, such coupling—mediated by lattice vibrations—strongly affects coherence and relaxation in quantum devices. When the bath is purely harmonic, energy is carried by ballistic phonons that propagate through the solid without scattering. Introducing anharmonicity leads to dissipative transport: nonlinear interactions induce multi–phonon scattering processes that enable low-frequency transitions, close any existing spectral gap, and allow dissipation even where it is forbidden in the harmonic case. Using a microscopic framework, we analyze how anharmonicity modifies the bath’s spectral properties and, consequently, the system’s dynamics within the Lindblad master equation framework. As a minimal model, we consider a modified spin-boson model in which a two-level system (TLS) is bilinearly coupled to a semi-infinite anharmonic chain of quantum oscillators. We find that bath anharmonicities lead the TLS damping rates to scale quadratically with temperature for gapped baths and introduce corrections of the same order to the leading linear dependence in the gapless case.