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

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.

References in corpus (16)

• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• Phase diagram of the one-dimensional half-filled extended Hubbard model
• First-principles dynamics of electrons and phonons
• NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods
• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model
• Exploring approximations to the GW self-energy ionic gradients
• Efficient and Stochastic Multireference Perturbation Theory for Large Active Spaces within a Full Configuration Interaction Quantum Monte Carlo Framework
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• Combined unitary and symmetric group approach applied to low-dimensional spin systems
• Exact diagonalization solver for the extended dynamical mean-field theory
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity