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

TL;DR

This paper extends full configuration interaction quantum Monte Carlo (FCIQMC) to coupled electron-boson systems, enabling unbiased energy calculations in models with infinite bosonic spaces and demonstrating its effectiveness in Hubbard-Holstein and quantum embedding models.

Contribution

The authors develop algorithmic modifications to FCIQMC allowing it to handle coupled fermion-boson Hamiltonians without truncating boson occupation, broadening its applicability.

Findings

Achieved unbiased energies in the Hubbard-Holstein model without additional computational costs.

Successfully sampled electron-boson Hamiltonians with a sign problem, reconstructing reduced density matrices.

Demonstrated FCIQMC's effectiveness as a solver within quantum embedding schemes.

Abstract

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. Secondly, 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 plasmonic-like 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.