Monte Carlo Methods in the Manifold of Hartree-Fock-Bogoliubov Wave Functions

TL;DR

This paper proposes a novel Monte Carlo approach to explore the manifold of Hartree-Fock-Bogoliubov wave functions, enabling the study of complex pairing mechanisms in quantum many-body systems.

Contribution

It introduces a method to perform random walks in the HFB wave function space, extending quantum Monte Carlo techniques to systems with complex pairing phenomena.

Findings

Demonstrates the feasibility of imaginary-time evolution in HFB states

Extends quantum Monte Carlo methods to complex pairing systems

Provides illustrative examples of the approach

Abstract

We explore the possibility to implement random walks in the manifold of Hartree-Fock-Bogoliubov wave functions. The goal is to extend state-of-the-art quantum Monte Carlo approaches, in particular the constrained-path auxiliary-field quantum Monte Carlo technique, to systems where finite pairing order parameters or complex pairing mechanisms, e.g., Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing or triplet pairing, may be expected. Leveraging the flexibility to define a vacuum state tailored to the physical problem, we discuss a method to use imaginary-time evolution of Hartree-Fock-Bogoliubov states to compute ground state correlations, extending beyond situations spanned by current formalisms. Illustrative examples are provided.