https://cnrs.hal.science/hal-03368550Carlen, Eric A.Eric A.CarlenRutgers - Rutgers University SystemHolzmann, MarkusMarkusHolzmannLPM2C - Laboratoire de physique et modélisation des milieux condensés - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble AlpesILL - Institut Laue-LangevinJauslin, IanIanJauslinDPPU - Department of Physics, Princeton University - Princeton University Lieb, Elliott H.Elliott H.LiebDepartments of Physics and Mathematics - Princeton University Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracyHAL CCSD2021[PHYS.COND] Physics [physics]/Condensed Matter [cond-mat]Holzmann, Markus2021-10-06 18:50:392023-03-13 10:58:162021-10-06 18:55:13enJournal articleshttps://cnrs.hal.science/hal-03368550/document10.1103/PhysRevA.103.053309application/pdf1In 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.