A simple renormalization group approximation of the groundstate properties of interacting bosonic systems

TL;DR

This paper introduces a simple renormalization group approach for analyzing the groundstate properties of interacting bosonic systems, enabling more accurate results than mean-field methods for large systems.

Contribution

The paper presents a new, easy-to-implement renormalization group method that improves groundstate property calculations beyond mean-field approximations for bosonic systems.

Findings

More accurate groundstate one-particle density matrix than Gross-Pitaevskii

Obtained Hall-Post lower bounds for groundstate energy

Applicable to large systems via numerical diagonalization

Abstract

We present a new, simple renormalization group method of investigating groundstate properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large systems. It is conceptually simple and easy to implement, and allows to investigate the properties unavailable through mean field approximations, such as one- and two-particle reduced density matrices of the groundstate. As an example, we model a weakly interacting 1D Bose gas in a harmonic trap. Compared to the mean-field Gross-Pitaevskii approximation, our method provides a more accurate description of the groundstate one-particle density matrix. We have also obtained the Hall-Post lower bounds for the groundstate energy of the gas. All results have been obtained by the straightforward numerical diagonalization of the Hamiltonian matrix.