Solution of the ‘sign problem’ in the path integral Monte Carlo simulations of strongly correlated Fermi systems: thermodynamic properties of helium-3

Abstract

A quantum path integral Monte Carlo approach [J. Phys. A 55, 035001 (2021)] for strongly correlated degenerate fermions has been modified to solve the ‘fermionic sign problem’. The exchange interaction of fermions was presented in the form of a positive semidefinite Gram determinant which significantly simplified the calculations. The verification of this approach has been carried out by comparison of the calculated equation of state with experimental data for quantum and degenerate unpolarised ${}^3\mathrm{He}$. The obtained results agree with experimental data in a wide range of reduced inverse density $0.4\le v^{\ast }\le 7.5$ and temperature $1\mathrm{K}\le T\le 13\mathrm{K}$. The range includes the gaseous and liquid states as well as the regions of the respective phase transition and the critical point. For the first time spin-resolved pair distribution functions have been calculated to analyse the spatial arrangement of helium atoms. The calculated internal energy has been presented for the gaseous region of quantum ${}^3\mathrm{He}$. The simulations have been carried out for the Lennard–Jones (LJ) potential with parameters $\sigma =2.71$ Å and $ϵ=6.68$ K.

GRAPHICAL ABSTRACT

Keywords:

• Helium-3
• path integral Monte Carlo
• sign problem

Acknowledgments

We acknowledge stimulating discussions with Prof. M. Bonitz, T. Schoof, S. Groth and T. Dornheim (Kiel).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the by the Russian Science Foundation [grant number 20-42-04421].