HiddenSp(2s+ 1)- orSO(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 · · · 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.

Critical phenomena in one dimension from a Bethe ansatz perspective

“…The spinor Bose gases with spinindependent short range interaction have a ferromagnetic ground state, [75,76]. This nature was well invested in the two-component spinor Bose gas with spinindependent s-wave scattering [77][78][79] and the integrable multi-component Bose gases [83,85]. At low energy level, the 1D two-component spinor Bose gas can be described by an effective Hamiltonian with spin-charge separation [79,80], i.e.…”

Symplectic Fermi liquid and its realization in cold atomic systems

“…More recently 24 the presence of symplectic symmetry in higherspin Hubbard models within cold fermions was discussed, and it is pointed out that the symplectic symmetry does not require any fine tuning for f = 3/2, while higher hyperfine spin systems require certain tuning of the interactions for the symmetry to be present. Another subgroup of SU(N) is SO(N), which can also be realized in cold atomic systems with bosonic isotopes 25 .…”

Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

“…In contrast to the two-component Fermi gases [22], the two-component spinor Bose gas with spin-independent s-wave scattering [23][24][25] has a ferromagnetic ground state as long as the interaction is fully spin independent. However, 1D spinor Bose gases with short-range density-density and spin-exchange interactions [26,27] can display a different ground state, i.e., either a ferromagnetic or an antiferromagnetic ground state solely depending on the spin-exchange interaction. In this context, the spin-1 spinor Bose gas with a short-range δ-function interaction and antiferromagnetic spin-spin interaction is particularly interesting due to the existence of various phases of quantum liquids associated with the Bethe ansatz (BA) * xwe105@physics.anu.edu.au solutions [26,[28][29][30].…”

“…In contrast to the two-component Fermi gases [22], the twocomponent spinor Bose gas with spin-independent s-wave scattering [23][24][25] has a ferromagnetic ground state as long as the interaction is fully spin independent. However, 1D spinor Bose gas with short-range density-density and spin-exchange interactions [26,27] can display a dif- * xwe105@physics.anu.edu.au 8) and (10), respectively. The V − S and V − F boundaries are given in (6).…”