Properties of fermionic systems with the Path-integral ground state method

TL;DR

This paper introduces FN-PIGS, a quantum Monte Carlo method combining path-integral ground state techniques with fixed-node approximation to accurately study fermionic and bosonic many-body systems at zero temperature.

Contribution

The paper develops and demonstrates FN-PIGS, a novel approach that effectively handles fermionic sign problems and allows unbiased property estimation at zero temperature.

Findings

Successfully applied to helium systems, capturing key quantum features.

Resolved sign problem in fermionic helium-3 systems.

Accurately computed pair correlation functions and kinetic energies.

Abstract

We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure $^4$He systems demonstrate most of the features of the method. Complementarily, for pure $^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate $^3$He-$^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T=0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the $^3$He kinetic energy in the mixture.