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arXiv:0902.0388 · Physical Review B

Dispersive spectrum and orbital order of spinless p -band fermions in an optical lattice

Xiancong Lu, Enrico Arrigoni

Published Jun 8, 2009• 17 citations
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Abstract

We study single-particle properties of a spinless $p$-band correlated fermionic gas in an optical lattice by means of a variational cluster approach (VCA). The single-particle spectral function is almost flat at half filling and develops a strongly dispersive behavior at lower fillings. The competition between different orbital orderings is studied as a function of filling. We observe that an ``antiferromagnetic'' orbital order develops at half filling and is destroyed by doping the system evolving into a disordered orbital state. At low-filling limit, we discuss the possibility of ``ferromagnetic'' orbital order by complementing the VCA result with observations based on a trial wave function. We also study the behavior of the momentum distribution for different values of the on-site interaction. Finally, we introduce an integration contour in the complex plane which allows to efficiently carry out Matsubara frequency sums.

DOI
10.1103/physrevb.79.245109

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We study Fermi gases in a three-dimensional cubic optical lattice with five fermions per site, i.e., the sss band is completely filled and the ppp band with threefold degeneracy is half filled. We show that for repulsive interaction between fermions, the system will exhibit spin-3/2 antiferromagnetic order at low temperature. This conclusion is obtained both in strong interaction regime by strong coupling expansion and in weak interaction regime by the Hartree--Fock mean-field theory with analysis of the Fermi surface nesting. We also show that in the strongly correlated regime the N\'eel temperature for ppp band antiferromagnetism is 2 to 3 orders of magnitudes higher than that of sss band, which is much more promising to be attained in cold atom experiments.
A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.
We study the ground-state properties of the interacting spinless fermions in the px,y{p}_{x,y}px,y​-orbital bands in the two-dimensional honeycomb optical lattice, which exhibit different features from those in the pz{p}_{z}pz​-orbital system of graphene. In addition to two dispersive bands with Dirac cones, the tight-binding band structure exhibits another two completely flat bands over the entire Brillouin zone. With the realistic sinusoidal optical potential, the flat bands acquire a finite but much smaller bandwidth compared to the dispersive bands. The band flatness dramatically enhanced interaction effects giving rise to various charge and bond ordered states at commensurate fillings of n=i6(i=1−−6)n=\frac{i}{6}(i=1--6)n=6i​(i=1−−6). At n=16n=\frac{1}{6}n=61​, the many-body ground states can be exactly solved as the close-packed hexagon states which can be stabilized even in the weakly interacting regime. The dimerization of bonding strength occurs at both n=12n=\frac{1}{2}n=21​ and 56\frac{5}{6}65​, and the latter case is accompanied with the charge-density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at n=13,23n=\frac{1}{3},\frac{2}{3}n=31​,32​. These crystalline orders exhibit themselves in the noise correlations of the time-of-flight spectra.
Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin-32\frac{3}{2}23​ fermionic atoms in optical lattices. When the sss-wave scattering lengths for the total spin S=2,0S=2,0S=2,0 satisfy conditions a2>a0>0{a}_{2}>{a}_{0}>0a2​>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-12\frac{1}{2}21​ 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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Abstract In this paper, we have studied spinless fermions in four specific quasi one-dimensional systems that are known to host flat bands in the noninteracting limit: the triangle lattice, the stub lattice, the diamond lattice, and the diamond lattice with transverse hopping. The influence of the nearest neighbour interaction on the flat bands was investigated. We used exact diagonalization of finite size lattices employing the Lanczos technique and determine the single particle spectral functions of the interacting system. Our results are compared with mean field calculations. In the cases of the triangle lattice and the stub lattice we found that the flat bands become dispersive in the presence of a finite interaction. For the diamond lattice and the diamond lattice with transverse hopping, we demonstrated that the flat bands are robust under the influence of the interaction in certain parameter ranges. Such systems could be realised experimentally with cold atoms in optical lattices.