Full configuration interaction quantum Monte Carlo for coupled electron-boson systems and infinite spaces

We extend the scope of full configuration interaction quantum Monte Carlo (FCIQMC) to be applied to coupled fermion-boson Hamiltonians, alleviating the a priori truncation in boson occupation which is necessary for many other wave-function-based approaches to be tractable. Detailing the required algorithmic changes for efficient excitation generation, we apply FCIQMC in two contrasting settings. The first is a sign-problem-free Hubbard-Holstein model of local electron-phonon interactions, where we show that, with care to control for population bias via importance sampling and/or reweighting, the method can achieve unbiased energies extrapolated to the thermodynamic limit, without suffering additional computational overheads from relaxing boson occupation constraints. Second, we apply the method as a "solver" within a quantum embedding scheme which maps electronic systems to local electron-boson auxiliary models, with the bosons representing coupling to long-range plasmoniclike fluctuations. We are able to sample these general electron-boson Hamiltonians with ease despite a formal sign problem, including a faithful reconstruction of converged reduced density matrices of the system.