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

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.

40 pages, 11 figures

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