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