Spin-quadrupole ordering of spin- (3)/(2) ultracold fermionic atoms in optical lattices in the one-band Hubbard model
Abstract
Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin- (3)/(2) fermionic atoms in optical lattices. When the s -wave scattering lengths for the total spin S=2,0 satisfy conditions a2>a0>0 , we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a two-dimensional square lattice, the saddle-point solution yields a staggered spin-quadrupole ordering at zero temperature with symmetry breaking from SO(5) to SO(4). Both spin and spin-quadrupole static structure factors are calculated, displaying highly anisotropic spin antiferromagnetic fluctuations and antiferroquadrupole long-range correlations, respectively. When Gaussian fluctuations around the saddle point are taken into account, spin-quadrupole density waves with a linear dispersion are derived. Compared with the spin-density waves in the half filled spin- (1)/(2) Hubbard model, the quadrupole density wave velocity is saturated in the strong-coupling limit, and there are no transverse spin-quadrupole mode couplings, as required by the SO(4) invariance of the effective action. Finally, in the strong-coupling limit of the model Hamiltonian, we derive the effective hyperfine spin-exchange interactions for the Mott insulating phases in the quarter filled and half filled cases, respectively.
- Publication:
-
Physical Review B
- Pub Date:
- November 2006
- DOI:
- 10.1103/PhysRevB.74.174404
- arXiv:
- arXiv:cond-mat/0608673
- Bibcode:
- 2006PhRvB..74q4404T
- Keywords:
-
- 71.10.Fd;
- 02.70.Ss;
- Lattice fermion models;
- Quantum Monte Carlo methods;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 12 pages, 5 figures