Variational Bethe Ansatz approach for dipolar one-dimensional bosons

TL;DR

This paper introduces a variational method based on the Bethe Ansatz to estimate the ground state energy of one-dimensional dipolar bosons, providing insights into their quantum properties and stability.

Contribution

It develops a novel variational approximation using the Bethe Ansatz for dipolar bosons, enabling analysis of their ground state energy and related properties.

Findings

Ground state energy per unit length calculated for dipolar bosons.

Tomonaga-Luttinger exponent as a function of density derived.

Predicted instability at a critical density for attractive interactions.

Abstract

We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length. This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta. Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.