Spin and charge correlations in the Hubbard model: a cold atoms perspective

Understanding the phases and correlations of strongly correlated systems is a longstanding problem. A paradigmatic description of such systems is provided by simplified models such as the Hubbard model. This model, which has the essential ingredients of a band (described by a tight binging hopping t) and (local) interactions (denoted U) has been shown to exhibit many of the features of more realistic condensed matter systems such as a Mott transition at half filling (one particle per site) and antiferromagnetic correlations. The model is indeed reducible to an Heisenberg model with a magnetic exchange J ⇠ 4t2/U in that limit. Upon doping the properties of the Hubbard model are still a challenge with reliable solutions only existing in one and infinite dimensions. Besides analytical or numerical approaches, a route to tackle such models has recently been provided by experiments on cold atomic systems. Indeed the use of optical lattices and of Feschbach resonances allows to realize a near ideal system of particles hopping on a tight-binding lattice, and to control the hopping t and the interaction U at will – providing an excellent realization of the Hubbard model [1]. Experiments on 6Li atoms have shown that realizing the fermionic Hubbard model was indeed possible and have evidenced the existence of an incompressible Mott insulator phase at half filling [2, 3]. Going beyond, and in particular even showing the existence of the antiferromagnetic correlations (not to even mention the properties of the doped phases) has however proven to be extremely challenging. This is due to two severe limitations of the cold atoms realization: