TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.2.031
TI  - Properties of fermionic systems with the path-integral ground state method
PY  - 2023/04/20
UR  - https://scipost.org/SciPostPhysCore.6.2.031
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 2
SP  - 031
A1  - Ujevic, Sebastian
AU  - Zampronio, Vinicius
AU  - de Abreu, Bruno R.
AU  - Vitiello, Silvio A.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.2.031,
	title={{Properties of fermionic systems with the path-integral ground state method}},
	author={Sebastian Ujevic and  Vinicius Zampronio and  Bruno R. de Abreu and  Silvio A. Vitiello},
	journal={SciPost Phys. Core},
	volume={6},
	pages={031},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.2.031},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.2.031},
}