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arXiv:0802.3211 · New Journal of Physics

Antiferromagnetic order of strongly interacting fermions in a trap: real-space dynamical mean-field analysis

Michiel Snoek, Irakli Titvinidze, Csaba Tőke, Krzysztof Byczuk, Walter Hofstetter

Published Sep 10, 2008• 152 citations
arXivHTMLPDF

Abstract

We apply dynamical mean-field theory to strongly interacting fermions in an inhomogeneous environment. With the help of this real-space dynamical mean-field theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin- in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.

DOI
10.1088/1367-2630/10/9/093008

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We apply dynamical mean-field theory to strongly interacting fermions in an inhomogeneous environment. With the help of this real-space dynamical mean-field theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin- in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.
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 propose a real-space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin-½ trapped in an optical lattice with a harmonic confinement. Using the real-space Gutzwiller variational approach, we find that in a system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring, and the antiferromagnetic order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the real-space dynamical mean-field theory approach. We also investigate the imbalanced case and find that the antiferromagnetic order is suppressed there.
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 review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.
We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory. Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.
We investigate the magnetic shell structure of repulsively interacting two-component Fermi gases trapped in a two-dimensional harmonic potential and loaded on the optical Lieb lattices. We employ the real-space dynamical mean-field theory (R-DMFT) to explicitly consider the trap potential in a self-consistent way. Computing the profiles of particle density and local magnetization across the lattice sites in the trap, we find that the incompressible core with ferrimagnetic ordering appears with the density plateau at the trap center, which is surrounded by the shell of the normal metallic phase. We examine the incompressibility of the core by adding more particles and creating the higher spin-population imbalance. While the core area expands from the outer shell with added particles and increased polarization, the excess particles are prohibited from going inside the core, and thus the density plateau is unchanged at the half-filling with the same magnetic ordering. In addition, we find that the feature of the phase separation differs with the sublattices, where the interstitial sites causing the flat band dispersion shows the signature of the abrupt transition in the density and magnetization at the boundary between the core and surrounding shells.