Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons

TL;DR

This paper uses exact numerical diagonalization to analyze the low-energy properties of small systems of interacting bosons in harmonic traps, comparing results with mean-field predictions and exploring effects of interaction strength and particle number.

Contribution

It provides a detailed numerical study of trapped interacting bosons, offering insights beyond mean-field approximations for small systems in one and two dimensions.

Findings

Ground state energies and densities are computed for various interaction strengths and particle numbers.

The dependence of properties on the product Ng is confirmed and analyzed.

Specific heat is calculated from the energy spectra.

Abstract

We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the ground state energy and density profile. We discuss the dependence of these quantities on both interaction strength g and particle number N. The ground state properties are compared to the predictions of the Gross-Pitaevskii equation, which depends on these parameters only through the combination Ng. We also calculate the specific heat based on the obtained energy spectra.