Affiliation:
1. Fluminense Federal University
2. University of Utrecht
3. University of Illinois at Urbana Champaign
4. State University of Campinas
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 ^44He systems demonstrate most of the features of the method. Complementarily, for pure ^33He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate ^33He-^44He mixtures, demonstrating the method’s robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature T = 0T=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 ^33He kinetic energy in the mixture.
Funder
Fundação de Amparo à Pesquisa do Estado de São Paulo
Instituto Serrapilheira
Netherlands Organization for International Cooperation in Higher Education
Subject
Statistical and Nonlinear Physics,Atomic and Molecular Physics, and Optics,Nuclear and High Energy Physics,Condensed Matter Physics