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arXiv:0710.3852 · Physical Review B

Theory of quantum antiferromagnetism of fermions in an optical lattice with a half-filled p band

Kai Wu, Hui Zhai

Published May 29, 2008• 34 citations
arXivHTMLPDF

Abstract

We study Fermi gases in a three-dimensional cubic optical lattice with five fermions per site, i.e., the $s$ band is completely filled and the $p$ 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 $p$ band antiferromagnetism is 2 to 3 orders of magnitudes higher than that of $s$ band, which is much more promising to be attained in cold atom experiments.

DOI
10.1103/physrevb.77.174431

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We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction.
We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the article, we perform unrestricted Hartree-Fock calculations for the two-dimensional (2D) case and find that above a critical interaction strength Uc{U}_{c}Uc​ the system turns ferromagnetic at the edge of the trap, which is in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For U<UcU<{U}_{c}U<Uc​, we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime, the same qualitative behavior is expected for 2D and three-dimensional (3D) systems. In the second part of the article, we give a general discussion of magnetic structures above Uc{U}_{c}Uc​. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the N\'eel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.
We study various Mott insulating phases of interacting spin-32\frac{3}{2}23​ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.
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Abstract We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x - and y -directions and a possibly different hopping parameter tzt_ztz​ t z in the z -direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases tz=0t_z=0tz​=0 t z = 0 and tz=tt_z=ttz​=t t z = t , respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that t=1t=1t=1 t = 1 , we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U , and on the hopping parameter tzt_ztz​ t z . We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as tz→0t_z \rightarrow 0tz​→0 t z → 0 . It is found that the asymptotic formulas are qualitatively different for tz=0t_z = 0tz​=0 t z = 0 (the two-dimensional case) and tz>0t_z > 0tz​>0 t z > 0 (the case of nonzero hopping in the z -direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit tz→0t_z \rightarrow 0tz​→0 t z → 0 in which the three-dimensional model reduces to the two-dimensional model.