We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to one (infinity). As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the non-local correlations suppress the CDW transition temperature.Introduction. Strongly interacting electron systems have been on the forefront of theoretical and experimental interest for several decades. This interest has intensified with the discovery of a variety of Heavy Fermion and related non Fermi liquid systems and the high-T c superconductors. In all these systems strong electronic interactions play a dominant role in the selection of at least the low temperature phase. The simplest theoretical models of strongly correlated electrons, the Hubbard model (HM) and the periodic Anderson model (PAM), have remained unsolved in more than one dimension despite a multitude of sophisticated techniques introduced since the inception of the models.With the ground breaking work by Metzner and Vollhardt [1] it was realized that these models become significantly simpler in the limit of infinite dimensions, D = ∞. Namely, provided that the kinetic energy is properly rescaled as 1/ √ D, they retain only local, though nontrivial dynamics: The self energy is constant in momentum space, though it has a complicated frequency dependence. Consequently, the HM and PAM map onto a generalized single impurity Anderson model. The thermodynamics and phase diagram have been obtained numerically by quantum Monte Carlo (QMC) and other methods. [2][3][4] The name dynamical mean field approximation (DMFA) has been coined for approximations in which a purely local self energy (and vertex function) is assumed in the context of a finite dimensional electron system. While it has been shown that this approximation captures many key features of strongly correlated systems even in a finite dimensional context, the DMFA, which leads to an effective single site theory, has some obvious limitations. For example, the DMFA can not describe phases with explicitly nonlocal order parameters, such as d-wave superconductivity, nor can it describe

The asymmetric infinite-dimensional periodic Anderson model is examined with a quantum Monte Carlo simulation. For small conduction band filling, we find a severe reduction in the Kondo scale, compared to the impurity value, as well as protracted spin screening consistent with some recent controversial photoemission experiments. The Kondo screening drives a ferromagnetic transition when the conduction band is quarter-filled and both the RKKY and superexchange favor antiferromagnetism. We also find RKKY-driven ferromagnetic and antiferromagnetic transitions. 71.10.Fd, 71.27.+a, 75.20.Hr, 75.30.Kz, 75.30.Mb

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.Introduction The rich phenomenology of high-T c superconductors [1] has stimulated strong experimental and theoretical interest in the field of strongly correlated electron systems. Common to all high-T c systems is the presence of antiferromagnetic ordering in undoped samples in proximity to a superconducting phase with a d-wave order parameter and the normal state pseudogap dominating the physics in underdoped samples. A successful theory must describe all these fundamental features at the same time.The 2D Hubbard model in the intermediate coupling regime or closely related models like the t-J model are believed to capture the essential physics of the high-T c cuprates [2]. The antiferromagnetic phase of the cuprates is well understood. In the strong coupling limit U ≫ W , where U is the Coulomb repulsion and W the bare bandwidth, the undoped Hubbard model reduces to the Heisenberg model, which has been proven to describe the low energy spin fluctuations of the cuprate parent compounds. However, off half-filling there is no complete understanding of the superconducting phase or the normal state pseudogap in the intermediate coupling 2D Hubbard model.Finite size quantum Monte Carlo (QMC) calculations for the doped 2D Hubbard model in the intermediate coupling regime with U < ∼ W , support the idea of a spin fluctuation driven interaction mediating d-wave superconductivity [3]. However, the fermion sign problem and the fact that the number of degrees of freedom grows rapidly with the lattice size, limits these calculations to temperatures too high to study a possible transition [3]. These calculations are also restricted to relatively small system sizes making statements for the thermodynamic limit problematic, and inhibiting studies of the low energy physics.These shortcomings do not apply to the Dynamical Mean Field Approximation (DMFA), which is by construction in the thermodynamic limit. Unfortunately,

We present numerically exact predictions of the periodic and single-impurity Anderson models to address photoemission experiments on heavy Fermion systems. Unlike the single impurity model the lattice model is able to account for the enhanced intensity, dispersion, and apparent weak temperature dependence of the Kondo resonant peak seen in recent controversial photoemission experiments. We present a consistent interpretation of these results as a crossover from the impurity regime to an effective Hubbard model regime described by Nozieres.