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

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

2010-06-10

arxiv.org/abs/1006.2118v1

J. Phys. A: Math. Theor. 44 (2011) 345001

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages, 2 figures

Scientific paper

10.1088/1751-8113/44/34/345001

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.

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