HAL CCSD
Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
Carlen, Eric A.
Holzmann, Markus
Jauslin, Ian
Lieb, Elliott H.
Rutgers University System (Rutgers)
Laboratoire de physique et modélisation des milieux condensés (LPM2C ) ; Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
Institut Laue-Langevin (ILL)
Department of Physics, Princeton University (DPPU) ; Princeton University
Departments of Physics and Mathematics ; Princeton University
v4: change title
International audience
ISSN: 1050-2947
EISSN: 1094-1622
Physical Review A : Atomic, molecular, and optical physics
American Physical Society
hal-03368550
https://cnrs.hal.science/hal-03368550
https://cnrs.hal.science/hal-03368550/document
https://cnrs.hal.science/hal-03368550/file/PhysRevA.103.053309.pdf
https://cnrs.hal.science/hal-03368550
Physical Review A : Atomic, molecular, and optical physics, 2021, 103 (5), pp.053309. ⟨10.1103/PhysRevA.103.053309⟩
ARXIV: 2011.10869
info:eu-repo/semantics/altIdentifier/arxiv/2011.10869
DOI: 10.1103/PhysRevA.103.053309
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.103.053309
en
[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat]
info:eu-repo/semantics/article
Journal articles
In 1963, a Simple Approach was developed to study the ground state energy of an interacting Bose gas. It consists in the derivation of an Equation, which is not based on perturbation theory, and which gives the exact expansion of the energy at low densities. This Equation is expressed directly in the thermodynamic limit, and only involves functions of $3$ variables, rather than $3N$. Here, we revisit this approach, and show that the Equation yields accurate predictions for various observables for all densities. Specifically, in addition to the ground state energy, we have shown that the Simple Approach gives predictions for the condensate fraction, two-point correlation function, and momentum distribution. We have carried out a variety of tests by comparing the predictions of the Equation with Quantum Monte Carlo calculations, and have found remarkable agreement. We thus show that the Simple Approach provides a new theoretical tool to understand the behavior of the many-body Bose gas, not only in the small and large density ranges, which have been studied before, but also in the range of intermediate density, for which little is known.
2021
info:eu-repo/semantics/OpenAccess