Hidden Sp(2s+1)- or SO(2s+1)-symmetry and new exactly solvable models in ultracold atomic systems

TL;DR

This paper explores high spin ultracold atom models with specific contact interactions, revealing hidden symmetries and proposing new exactly solvable models solved via Bethe ansatz, with insights into their ground states.

Contribution

It identifies hidden Sp(2s+1) or SO(2s+1) symmetries in ultracold atom models and introduces a new class of exactly solvable models based on these symmetries.

Findings

Models exhibit Sp(2s+1) or SO(2s+1) symmetry in the spin sector.

New exactly solvable models are constructed and solved using Bethe ansatz.

Ground states for repulsive fermions are analyzed.

Abstract

The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found that those models have either $Sp(2s+1)$-symmetry for the fermions or $SO(2s+1)$-symmetry for the bosons in the spin sector. Based on the symmetry analysis, a new class of exactly solvable models is proposed and solved via the Bethe ansatz. The ground states for repulsive fermions are also discussed.