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

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 ansätze. 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.

35 pages, 2 figures, minor typos corrected

References in corpus (12)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Theory of Intertwined Orders in High Temperature Superconductors
• Superconductivity and Phase Diagram in the Iron-based Arsenic-oxides ReFeAsO1-delta (Re = rare earth metal) without F-Doping
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• The sign of the overlap of HFB wave functions
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
• Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: a variational study
• Cold Attractive Spin Polarized Fermi Lattice Gases and the Doped Positive U Hubbard Model
• Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method