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 \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.

12 pages, 5 figures

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• Ultracold fermions and the SU(N) Hubbard model
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• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Ultracold atomic Bose and Fermi spinor gases in optical lattices
• Competing orders in the generalized Hund chain model at half-filling
• Mott insulating phases and quantum phase transitions of interacting spin-3/2 fermionic cold atoms in optical lattices at half filling
• Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• The Symplectic Fermi Liquid and its realization in cold atomic systems
• Competing Valence Bond States of Spin-3/2 Fermions on a Strongly Coupled Ladder
• The Symmetry Principle in Condensed Matter Physics (I)
• Topological term in the non-linear $\sigma$ model of the SO(5) spin chains