A simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy

TL;DR

This paper revisits a 1963 simple theoretical approach to the interacting Bose gas, demonstrating its accuracy across all densities and validating it against Quantum Monte Carlo results for various physical observables.

Contribution

The paper shows that the Simple Approach yields accurate predictions for the Bose gas at all densities, including intermediate, by comparing with numerical simulations.

Findings

Accurate predictions for ground state energy across densities

Good agreement with Quantum Monte Carlo for condensate fraction

Reliable estimates of correlation functions and momentum distribution

Abstract

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.