Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model

Details Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model

2006-08-30

arxiv.org/abs/cond-mat/0608673v3

Phys. Rev. B 74, 174404 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, 5 figures

Scientific paper

10.1103/PhysRevB.74.174404

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 \textit{s}-wave scattering lengths for the total spin $S=2,0$ satisfy conditions $a_{2}>a_{0}>0$, we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a 2D 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.

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