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

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.

6 pages, 2 figures

References in corpus (4)

• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions
• Simultaneous Magneto-Optical Trapping of Bosonic and Fermionic Chromium Atoms
• Valence bond solid states with symplectic symmetry

Cited by in corpus (6)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Critical phenomena in one dimension from a Bethe ansatz perspective
• Fermi gas with attractive potential and arbitrary spin in one-dimensional trap
• Exotic pairing in 1D spin-3/2 atomic gases with $SO(4)$ symmetry
• Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction
• The Symplectic Fermi Liquid and its realization in cold atomic systems