Another important physical system, usually described by effective field theories of Hubbard type, is that of ultracold fermionic quantum gases. In contradistinction to the description of electrons in solids, in the case of ultracold quantum gases one has to take into account also the effects of a harmonic trap and an optical lattice. The presence of a harmonic trap obviously makes the investigation of the properties of such quantum gases more complicated, since it breaks translational invariance and, hence, causes the physical properties of the gas to be explicitly site dependent. There are various methods available for the study of low temperature properties of fermionic quantum gases.
In both papers cited below we used perturbative techniques. While the starting point of these investigations is the saddle point (Hartree-Fock) approximation, it is possible to take into account also contributions and effects from quantum fluctuations. An important finding from the second of these two papers, which was also selected for the October issue of the "Virtual Journal of Atomic Quantum Fluids", is the transverse nature of the antiferromagnetic order parameter in unbalanced systems:
Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases
T. Gottwald and P. G. J. van Dongen, Eur. Phys. J. B 61, 277-285 (2008)
Antiferromagnetic Order of Repulsively Interacting Fermions on Optical lattices
Tobias Gottwald and Peter van Dongen
Phys. Rev. A 80, 033603 (2009)
T. Gottwald and P. G. J. van Dongen, Eur. Phys. J. B 61, 277-285 (2008)
Antiferromagnetic Order of Repulsively Interacting Fermions on Optical lattices
Tobias Gottwald and Peter van Dongen
Phys. Rev. A 80, 033603 (2009)