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arXiv:0903.5265 · Physical Review A

Antiferromagnetic order of repulsively interacting fermions on optical lattices

Tobias Gottwald, P. G. J. van Dongen

Published Sep 9, 2009• 15 citations
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Abstract

The N\'eel state in fermionic mixtures of two pseudospin species in an optical lattice is analyzed at low temperatures. Experimentally it remains a challenge to demonstrate antiferromagnetic correlations in ultracold fermionic quantum gases. We find that, while in balanced systems the N\'eel order parameter can point in any spatial direction, in imbalanced mixtures antiferromagnetism is strictly perpendicular to the quantization axis (i.e., the $z$ axis). Since, experimentally, one always has to assume some minimal imbalance this should have important consequences for ongoing experiments.

DOI
10.1103/physreva.80.033603

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The N'eel state in fermionic mixtures of two pseudospin species in an optical lattice is analyzed at low temperatures. Experimentally it remains a challenge to demonstrate antiferromagnetic correlations in ultracold fermionic quantum gases. We find that, while in balanced systems the N'eel order parameter can point in any spatial direction, in imbalanced mixtures antiferromagnetism is strictly perpendicular to the quantization axis (i.e., the zzz axis). Since, experimentally, one always has to assume some minimal imbalance this should have important consequences for ongoing experiments.
The exchange coupling between quantum mechanical spins lies at the origin of quantum magnetism. We report on the observation of nearest-neighbor magnetic spin correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy within the lattice structure. This is achieved in a tunable-geometry optical lattice, which also enables the detection of the magnetic correlations. We load a low-temperature two-component Fermi gas with repulsive interactions into either a dimerized or an anisotropic simple cubic lattice. For both systems the correlations manifest as an excess number of singlets as compared to triplets consisting of two atoms with opposite spins. For the anisotropic lattice, we determine the transverse spin correlator from the singlet-triplet imbalance and observe antiferromagnetic correlations along one spatial axis. Our work paves the way for addressing open problems in quantum magnetism using ultracold fermions in optical lattices as quantum simulators.
We investigate antiferromagnetic order of repulsively interacting fermionic atoms in an optical lattice by means of dynamical mean-field theory (DMFT). Special attention is paid to the case of an imbalanced mixture. We take into account the presence of an underlying harmonic trap, both in a local-density approximation and by performing full real-space DMFT calculations. We consider the case in which the particle density in the trap center is at half-filling, leading to an antiferromagnetic region in the center, surrounded by a Fermi liquid region at the edge. In the case of an imbalanced mixture, the antiferromagnetism is directed perpendicular to the ferromagnetic polarization and canted. We pay special attention to the boundary structure between the antiferromagnetic and the Fermi liquid phase. For the moderately strong interactions considered here, no Stoner instability toward a ferromagnetic phase is found. Phase separation is only observed for strong imbalance and sufficiently large repulsion.
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a directly observable signature of the ordered state. For the trapped system, we compare our results obtained by real-space DMFT to a local-density approximation. We calculate the entropy for a wide range of parameters and identify regions, in which mass-imbalanced mixtures could have clear advantages over balanced ones for the purpose of obtaining and detecting quantum magnetism.
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis for a gas confined in a harmonic trap, both within the local density approximation and using a full real-space generalization of DMFT.
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.
We theoretically investigate, using nonperturbative strong correlation techniques, Mott-insulating phases and magnetic ordering of two-component fermions in a two-dimensional double-well optical lattice. At filling of two fermions per site, there are two types of Mott insulators, one of which is characterized by spin-1 antiferromagnetism below the N\'eel temperature. The superexchange interaction in this system is induced by the interplay between the interband interaction and the spin degree of freedom. A great advantage of the double-well optical lattice is that the magnetic quantum phase diagram and the N\'eel temperature can be easily controlled by tuning the orbital energy splitting of the two-level system. Particularly, the N\'eel temperature can be one order of magnitude larger than that in standard optical lattices, facilitating the experimental search for magnetic ordering in optical lattice systems.