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arXiv:hep-lat/0409060 · Nuclear Physics B - Proceedings Supplements

Exploring Lattice Methods for Cold Fermionic Atoms

Matthew Wingate A

Published Jan 15, 2005• 1 citation
arXivHTMLPDF
DOI
10.1016/j.nuclphysbps.2004.11.139

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Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lectures start with basic considerations on energy scales, and on the regimes in which a description by an effective Hubbard model is valid. Qualitative ideas about the Mott transition are then presented, both for bosons and fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism of the fermionic Hubbard model at half-filling is briefly reviewed. The possibility that interaction effects facilitate adiabatic cooling is discussed, and the importance of using entropy as a thermometer is emphasized. Geometrical frustration of the lattice, by suppressing spin long-range order, helps revealing genuine Mott physics and exploring unconventional quantum magnetism. The importance of measurement techniques to probe quasiparticle excitations in cold fermionic systems is emphasized, and a recent proposal based on stimulated Raman scattering briefly reviewed. The unconventional nature of these excitations in cuprate superconductors is emphasized.
Ultra-cold fermionic atoms trapped in optical lattices may be a candidate for the discovery of new novel phenomena in condensed matter systems.Experiments afford the creation of virtually any lattice geometry, and physicalparameters of tight binding type lattice models can be acurately and easily tuned. Although some theoretical work has been conducted, few have used the power of the functional renormalization group method to unearth rigorous methods for determining collective many-body phases in this regime. Motivated byrecent theoretical achievements, we investigate novel condensed matter systemsinvolving interacting fermions which are engineered to be confined in differentdimensions. In this sense, we seek low energy effective theories for low-dimensional fermionic lattice systems embedded into higher dimensional lattice systems, and show how tuning physical quantities, such as the fillingor density, can have dramatic effects on the behavior of the lower dimensionalsystem.