A Note on the Construction of Trial States for the Dilute Bose Gas

TL;DR

This paper reviews a method for constructing trial states for the dilute Bose gas, simplifying the derivation of the Lee-Huang-Yang correction as an energy upper bound.

Contribution

It introduces a simplified approach to build trial states capturing correlations, leading to an easier derivation of the Lee-Huang-Yang correction.

Findings

Provides a simplified derivation of the Lee-Huang-Yang correction.

Uses local particle number cutoff to build correlated trial states.

Establishes an upper bound for the ground state energy in the thermodynamic limit.

Abstract

We review how the local particle number cutoff introduced in [11] is used to build trial states for the dilute Bose gas that capture the substantial correlation structure of the ground state in the thermodynamic limit. In particular, we provide a simplified derivation of the Lee-Huang-Yang correction as an upper bound for the ground state energy.