Non-ideal Boson system in the Gaussian approximation

TL;DR

This paper explores the ground-state and thermal properties of a non-ideal boson system using a self-consistent Gaussian mean-field approximation, revealing phases and a gapped quasi-particle spectrum.

Contribution

It introduces a comprehensive Gaussian approximation framework for interacting bosons, connecting with classical results and analyzing phase stability and excitation spectra.

Findings

Supports a free or unstable phase depending on interactions.

Generates a gapped quasi-particle spectrum in the effective theory.

Provides finite temperature results within a grand canonical approach.

Abstract

We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent gaussian mean-field approximation wich consists in writing the variational determined density operator as the most general gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee,Yang and Huang in terms of a particular truncations of the gaussian approximation. The full gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cut-off, the full gaussian approximation generates a quasi-particle spectrum having an energy gap.