The asymptotic Bethe ansatz solution for one-dimensional SU(2) spinor bosons with finite range Gaussian interactions

TL;DR

This paper introduces an exactly solvable one-dimensional SU(2) spinor boson model with finite range Gaussian interactions, deriving analytical expressions for ground state energy and chemical potential, and exploring effects on density profiles and condensation.

Contribution

It presents a novel exactly solvable model with finite range interactions using asymptotic Bethe ansatz, extending understanding of spinor bosons beyond zero-range potentials.

Findings

Derived analytical ferromagnetic ground state energy and chemical potential.

Finite range potentials influence density profiles and promote quasi Bose-Einstein condensation.

Model solvability established when interaction width is much smaller than inter-particle separation.

Abstract

We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a two-body finite range Gaussian interaction potential. We show that the model is exactly solvable when the width of the interaction potential is much smaller compared to the inter-particle separation. This model is then solved via the asymptotic Bethe ansatz technique. The ferromagnetic ground state energy and chemical potential are derived analytically. We also investigate the effects of a finite range potential on the density profiles through local density approximation. Finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials.