Extension of Dynamical Mean-Field Theory: Inclusion of Spatial Fluctuations

A hybrid approach that takes account of local and spatial fluctuations is proposed for strongly correlated electron systems. The spatial fluctuations are constructed in the framework of dynamical mean-field theory (DMFT), and they are utilized to improve the DMFT self-energy with nonlocal corrections via the exchange of the fluctuations. We demonstrate that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. Some future applications of the present theory are briefly discussed.