Fermionic atoms confined in a potential created by standing wave light can undergo a phase transition to a superfluid state at a dramatically increased transition temperature. Depending upon carefully controlled parameters, a transition to a superfluid state of Cooper pairs, antiferromagnetic states or d-wave pairing states can be induced and probed under realistic experimental conditions. We describe an atomic physics experiment that can provide critical insight into the origin of high-temperature superconductivity in cuprates.

We present a theoretical analysis of the phase diagram of two-component bosons on an optical lattice. A new formalism is developed which treats the effective spin interactions in the Mott and superfluid phases on the same footing. Using the new approach we chart the phase boundaries of the broken spin symmetry states up to the Mott to superfluid transition and beyond. Near the transition point, the magnitude of spin exchange can be very large, which facilitates the experimental realization of spin-ordered states. We find that spin and quantum fluctuations have a dramatic effect on the transition making it first order in extended regions of the phase diagram. For Mott states with even occupation we find that the competition between effective Heisenberg exchange and spindependent on-site interaction leads to an additional phase transition from a Mott insulator with no broken symmetries into a spin-ordered insulator. PACS numbers: PACS I. INTRODUCTIONRecent observations of the superfluid to Mott insulator transition in a system of ultracold atoms in an optical lattice open fascinating prospects for studying many-body phenomena associated with strongly correlated systems in a highly controllable environment [1, 2, 3]. For instance, theoretical studies have shown that, with spinor bosonic or fermionic atoms in optical lattices, it may be possible to observe complex quantum phase transitions [4], to realize novel superfluidity mechanisms [5], and to probe onedimensional systems exhibiting spin charge separation [6].Recently, Duan et al.[7] proposed a technique to implement interacting spin-1 2 Hamiltonians using ultra-cold atoms, opening the door to controlled studies of quantum magnetism. In this approach the two-state bosonic or fermionic atoms are confined in an optical lattice where spin-dependent interactions and hopping are controlled by adjusting the intensity, frequency, and polarization of the trapping light. Deep in the Mott phase the motional degrees of freedom are frozen out and the remaining spin degrees of freedom are coupled by an effective Heisenberg exchange. In refs. [7,8], an effective spin hamiltonian was derived by perturbation theory for the case of a single atom per site and the limit of small tunneling. However, in practice Mott states with more than one atom per site are also of considerable interest and may exhibit richer phase diagrams. Furthermore, spin effects are expected to be important, and even stronger, at larger values of the tunnelling, where perturbation theory fails. For example, an important question that cannot be addressed by the perturbative treatments is how spin affects the transition into a superfluid phase and the properties of the superfluid phase itself.In this paper we first extend the earlier approaches to the case of Mott states with general integer occupation. We find that at even fillings the competition between on-site interactions and nearest neighbor spin exchange leads to a transition from a spin ordered Mott state to one with no broken symmetries. Then we presen...

We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 two flavors remain half filled by cannibalizing the third flavor. For U<0 and odd N a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.