Properties of fermionic systems with the path-integral ground state method
Sebastian Ujevic, Vinicius Zampronio, Bruno R. de Abreu, Silvio A. Vitiello
SciPost Phys. Core 6, 031 (2023) · published 20 April 2023
- doi: 10.21468/SciPostPhysCore.6.2.031
- Submissions/Reports
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.
Cited by 1
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Sebastian Ujevic,
- 2 Vinicius Zampronio,
- 3 Bruno R. de Abreu,
- 4 Silvio A. Vitiello
- 1 Universidade Federal Fluminense / Fluminense Federal University [UFF]
- 2 Universiteit Utrecht / University of Utrecht [UU]
- 3 University of Illinois at Urbana Champaign [UIUC]
- 4 Universidade Estadual de Campinas / State University of Campinas [UNICAMP]