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

TL;DR

This paper introduces a diagrammatic Monte Carlo method for spin-boson models, enabling accurate analysis of light-matter interactions and emitter dynamics in waveguides across various coupling regimes.

Contribution

It develops a novel diagrammatic Monte Carlo algorithm with self-consistent vertices for general spin-boson models, extending strong-coupling expansion techniques.

Findings

Demonstrates convergence to exact results in diverse parameter regimes.

Reveals a delocalization-localization crossover in the spin at low temperatures.

Shows that emitter response can be modeled by an effective Rabi model in certain conditions.

Abstract

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