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

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 ingre-dient 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 4He systems demonstrate most of the features of the method. Complementarily, for pure 3He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate 3He-4He 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 ap-proximation; 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 3He kinetic energy in the mixture.

Automated summary

We investigate strongly correlated many-body systems of bosons and fermions using the path-integral ground state method (PIGS), incorporating the fixed-node approximation (FN-PIGS) to deal with Fermi-Dirac statistics. We discuss in detail the pair density matrices used to construct the full density operator in coordinate representation. We explore the proof-of-concept harmonic oscillator and the helium atom as a representative quantum many-body system, with pure 4He systems demonstrating the method's key features and pure 3He systems benefiting from the fixed-node approximation to resolve the sign problem.