Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

TL;DR

This paper introduces a stochastic Monte Carlo approach to many-body fermion systems using Hartree-Fock-Bogoliubov wave functions, enabling efficient treatment of pairing interactions and overcoming sign or phase problems.

Contribution

It develops a novel Monte Carlo method based on HFB states for interacting fermions, combining HFB theory with quantum Monte Carlo techniques.

Findings

Successfully applied to the Kitaev model for exact projection.

Demonstrated effectiveness in the Hubbard model with pairing fields.

Provided methods for state propagation, stabilization, and overlap computation.

Abstract

We describe the computational ingredients for an approach to treat interacting fermion systems in the presence of pairing fields, based on path-integrals in the space of Hartree-Fock-Bogoliubov (HFB) wave functions. The path-integrals can be evaluated by Monte Carlo, via random walks of HFB wave functions whose orbitals evolve stochastically. The approach combines the advantage of HFB theory in paired fermion systems and many-body quantum Monte Carlo (QMC) techniques. The properties of HFB states, written in the form of either product states or Thouless states, are discussed. The states are shown to be propagated by generalized one-body operators. The states can be stabilized for numerical iteration, and overlaps between two such states and one-body Green's functions can be computed. A constrained-path or phaseless approximation can be applied to the random walks of the HFB states if a sign problem or phase problem is present. The method is illustrated with an exact numerical projection in the Kitaev model, and in the Hubbard model with attractive interaction under an external pairing field.