Composite boson description of a low density gas of excitons

TL;DR

This paper investigates the properties of a low-density exciton gas, validating the composite boson model through quantum Monte Carlo simulations and scattering calculations, and comparing results with Bogoliubov theory.

Contribution

It provides a detailed analysis of exciton interactions and validates the composite boson description across different densities using advanced computational methods.

Findings

Agreement with Bogoliubov theory at low densities

Extraction of exciton-exciton scattering length

Good description of condensate fraction at low densities

Abstract

Ground state properties of a fermionic Coulomb gas are calculated using the fixed-node diffusion Monte Carlo method. The validity of the composite boson description is tested for different densities. We extract the exciton-exciton $s$-wave scattering length by solving the four-body problem in a harmonic trap and mapping the energy to that of two trapped bosons. The equation of state is consistent with the Bogoliubov theory for composite bosons interacting with the obtained $s$-wave scattering length. The perturbative expansion at low density has contributions physically coming from (a) exciton binding energy, (b) mean-field Gross-Pitaevskii interaction between excitons, (c) quantum depletion of the excitonic condensate (Lee-Huang-Yang terms for composite bosons). In addition, for low densities we find a good agreement with the Bogoliubov bosonic theory for the condensate fraction of excitons. The equation of state in the opposite limit of large density is found to be well described by the perturbative theory including (a) mixture of two ideal Fermi gases (b) exchange energy. We find that for low densities both energetic and coherent properties are correctly described by the picture of composite bosons (excitons).