Schedule Oct 15, 2010
Néel Transition of Lattice Fermions in a Harmonic Trap: A Real-Space Dynamic Mean-Field Study
Nils Bluemer (Johannes Gutenberg Univ.)

Elena V. Gorelik,1 Irakli Titvinidze,2 Walter Hofstetter,2 Michiel Snoek,3 and Nils Blümer,1

1 Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany
2 Institute for Theoretical Physics, Johann Wolfgang Goethe University, 60438 Frankfurt/Main, Germany
3 Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam, The Netherlands

Ultracold atoms on optical lattices are fascinating systems in their own right, giving access to a wide range of "exotic" physics including, e.g., color superconductivity. At the same time, their potential role as "quantum simulators" of condensed-matter system attracts enormous interest. A missing link in this context is the realization of antiferromagnetic (AF) Néel phases: in spite of extensive efforts, no AF signatures have been seen in experiments so far. These efforts have mostly concentrated on the achievement of low enough temperatures; however, the successful detection of AF phases or correlations will certainly also depend on a proper choice of observables. We extend the range of applicability of the recently developed real-space dynamical mean-field theory (DMFT) to the temperatures of experimental interest by combining it with a highly efficient quantum Monte Carlo algorithm [1]. Our massively parallel implementation scales to some 100 000 atoms on an optical lattice without significant approximations beyond DMFT. We demonstrate that the onset of AF correlations at low temperatures is signaled, for interactions , by a strongly enhanced double occupancy [2]. 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.

[1] N. Blümer and E. V. Gorelik, arXiv:1006.2716, [Comput. Phys. Commun., to be published; doi:10.1016/j.cpc.2010.07.011].

[2] E. V. Gorelik, I. Titvinidze, W. Hofstetter, M. Snoek, and N. Blümer, Phys. Rev. Lett. 105, 065301 (2010).

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