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We propose a diagrammatic Monte Carlo approach for general spin-boson models,which can be regarded as a generalization of the strong-coupling expansion forfermionic impurity models. The algorithm is based on a self-consistentlycomputed three-point vertex and a stochastically sampled four-point vertex, andachieves convergence to the numerically exact result in a wide parameterregime. The performance of the algorithm is demonstrated with applications to aspin-boson model representing an emitter in a waveguide. As a function of thecoupling strength, the spin exhibits a delocalization-localization crossover atlow temperatures, signaling a qualitative change in the real-time relaxation.In certain parameter regimes, the response functions of the emitter coupled tothe electromagnetic continuum can be described by an effective Rabi model withappropriately defined parameters. We also discuss the spatial distribution ofthe photon density around the emitter.

Vertex-based Diagrammatic Treatment of Light-Matter-Coupled Systems