Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions

TL;DR

This paper extends the phaseless quantum Monte Carlo method to include Hartree-Fock-Bogoliubov wavefunctions, enabling better simulation of superconducting systems with controlled statistical errors and efficient observable estimation.

Contribution

It introduces a stochastic HFB-based Monte Carlo approach for strongly correlated superconductors, improving upon existing methods by incorporating HFB vacua and Pfaffian techniques for observable calculations.

Findings

Applied to spin-polarized Hubbard model in the attractive regime

Demonstrated controlled statistical errors in simulations

Provided a compact Pfaffian-based expression for observables

Abstract

The so-called phaseless quantum Monte-Carlo method currently offers one of the best performing theoretical framework to investigate interacting Fermi systems. It allows to extract an approximate ground-state wavefunction by averaging independent-particle states undergoing a Brownian motion in imaginary-time. Here, we extend the approach to a random walk in the space of Hartree-Fock-Bogoliubov (HFB) vacua that are better suited for superconducting or superfluid systems. Well-controlled statistical errors are ensured by constraining stochastic paths with the help of a trial wavefunction, also guiding the dynamics and in the form of a linear combination of HFB ans\"atze. Estimates for the observables are reconstructed through an extension of Wick's theorem to matrix elements between HFB product states. The usual combinatory complexity associated to the application of this theorem for four- and more- body operators is bypassed with a compact expression in terms of Pfaffians. The limiting case of a stochastic motion within Slater determinants but guided with HFB trial wavefunctions is also considered. Finally, exploratory results for the spin polarized Hubbard model in the attractive regime are presented.