Abstract Ultracold atoms have attracted enormous interest recently, and Cooper pairing between fermionic alkali atoms may have been observed experimentally. Besides the demonstration of phenomena that we are acquainted with from solid state physics, ultracold atoms possibly exhibit interesting many‐body ground states that do not have straightforward counterparts in solid state physics. The hyperfine degree of freedom of the atoms in combination with optical lattices may allow for the approximate realization of fermionic SU(N) Hubbard models where N counts the number of trapped hyperfine states (‘flavors’). We analyze the ground states of this model on the two‐dimensional square lattice using one‐loop renormalization group and meanfield techniques. In the repulsive case for N > 6 and half band filling staggered flux order is found as the dominant instability, in agreement with the large‐N limit. In the attractive case and odd N a full Fermi surface coexists with a superfluid in the ground state. We describe how these unconventional paired states can be identified in the density response of the fermions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We explore ordering tendencies in weakly coupled Hubbard and t-J models on the two-dimensional square lattice for fermions with N flavors. Such systems may be realized using ultracold atoms with several hyperfine states in optical lattices. The analysis is based on a functional renormalization group approach. In the repulsive Hubbard model for N > 6 and half band filling staggered flux order is found as the dominant instability, in agreement with the large-N limit. In the t-J model without occupancy constraint this type of ground state is suggested already for N > 2. In the attractive case and odd N a full Fermi surface coexists with a superfluid in the ground state. We describe how these unconventional paired states can be identified in the density response of the fermions.
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal repulsive on-site interactions
U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., they should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a ``semicompressible'' state observed for large
U near half filling.