Pseudoparticle-operator description of an interacting Bose gas

TL;DR

This paper develops a pseudoparticle operator framework for the interacting Bose gas, enabling exact diagonalization and analysis of low-energy properties using Bethe ansatz techniques.

Contribution

It introduces a complete pseudoparticle operator algebra that diagonalizes the Bose gas Hamiltonian and describes excitations as composite and collective pseudoparticles.

Findings

All eigenstates generated by pseudoparticle operators.

Bosonic excitations are composites of pseudoparticles.

Framework allows calculation of static and dynamic properties.

Abstract

We write the Hamiltonian of the Bose gas with two-body repulsive $\delta$-function potential in a pseudoparticle operator basis which diagonalizes the problem via the Bethe ansatz. In this operator basis the original bosonic interactions are represented by zero-momentum forward-scattering interactions between Landau-liquid pseudoparticles. We find that this pseudoparticle operator algebra is complete: {\it all} the Hamiltonian eigenstates are generated by acting pseudoparticle operators on the system vacuum. It is shown that one boson of vanishing momentum and energy is a composite of a one-pseudoparticle excitation and a collective pseudoparticle excitation. These excitations have finite opposite momenta and cannot be decomposed. Our formalism enables us to calculate the various quantities which characterize the static and dynamic behavior of the system at low energies.