obtained by numerically solving self-consistent integral equations. Detailed comparisons with experimental results on transition-metal oxides have shown that three-dimensional materials can be well described by the infinite-dimensional self-consistent mean-field approach. [11] Other methods, such as slave-boson [12] or slave-fermion [13] approaches, have also allowed one to gain insights into the Hubbard model through various mean-field theories corrected for fluctuations. In this context however, the mean-field theories are not based on a variational principle. Instead, they are generally based on expansions in the inverse of a degeneracy parameter, [14] such as the number of fermion flavors N , where N is taken to be large despite the fact that the physical limit corresponds to a small value of this parameter, say N = 2. Hence these theories must be used in conjunction with other approaches to estimate their limits of validity. [15] Expansions around solvable limits have also been explored. [16] Finally, numerical solutions, [17] with proper account of finite-size effects, can often provide a way to test the range of validity of approximation methods independently of experiments on materials that are generally described by much more complicated Hamiltonians.Despite all this progress, we are still lacking reliable theoretical methods that work in arbitrary space dimension. In two dimensions in particular, it is believed that the Hubbard model may hold the key to understanding normal state properties of high-temperature superconductors. But even the simpler goal of understanding the magnetic phase diagram of the Hubbard model in two dimensions is a challenge. Traditional mean-field techniques, or even slaveboson mean-field approaches, for studying magnetic instabilities of interacting electrons fail in two dimensions. The Random Phase Approximation (RPA) for example does not satisfy the Pauli principle, and furthermore it predicts finite temperature antiferromagnetic or spin density wave (SDW) transitions while this is forbidden by the Mermin-Wagner theorem. Even though one can study universal critical behavior using various forms of renormalization group treatments [18] [19] [20] [21] [22] or through the self-consistent-renormalized approach of Moriya [23] which all satisfy the Mermin-Wagner theorem in two dimensions, cutoff-dependent scales are left undetermined by these approaches. This means that the range of interactions or fillings for which a given type of ground-state magnetic order may appear is left undetermined.Amongst the recently developed theoretical methods for understanding both collective and single-particle properties of the Hubbard model, one should note the fluctuation exchange approximation [24] (FLEX) and the pseudo-potential parquet approach.[25] The first one, FLEX, is based on the idea of conserving approximations proposed by Baym and Kadanoff. [26] [27] This approach starts with a set of skeleton diagrams for the Luttinger-Ward functional [28] to generate a self-energy that is compute...

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the Cellular Dynamical Mean Field Theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.PACS numbers: 71.10. Fd, 71.27.+a, 71.30.+h, The issue of the origin of the pseudogap phenomenon observed in underdoped cuprates lies at the center of any theoretical explanation for high temperature superconductivity in the cuprates and is one of the most challenging questions in condensed matter physics. The suppression of low energy spectral weight in the normal state of these materials has been observed through various experimental probes [1]. In spite of many theoretical works to explain the observed anomalies, there is no consensus at present. The lack of controlled approximations to deal with the strong coupling physics and low dimensionality inherent to these systems continues to pose major stumbling blocks towards a complete theoretical understanding. Since the parent compounds of the cuprates are Mott-Hubbard insulators, an understanding of such an insulator and its evolution into a correlated metal upon doping is crucial.In this paper we study the two-dimensional Hubbard model on a square lattice at and near half-filling with Cellular Dynamical Mean-Field Theory (CDMFT) [2]. The CDMFT method is a natural generalization of the single site DMFT [3] to incorporate short-range spatial correlations. Since at and near half-filling short-range spin correlations are dominant at low energy, this method is expected to describe additional features caused by spin degrees of freedom in the single-particle spectrum. The CDMFT [4] has already passed several tests against exact results obtained by the Bethe Ansatz and the Density Matrix Renormalization Group (DMRG) techniques in one dimension, where the CDMFT scheme is expected to be in the worst case scenario. Long-range order involving several lattice sites such as d-wave superconductivity can be also described in CDMFT [5]. Several other cluster schemes have been proposed [6,7,8,9, 10] including Dynamical Cluster Approximation (DCA) [7], Cluster Perturbation Theory (CPT) [8] and its variational extension (V-CPT) [9]. The variational principle used in the last scheme allows one to consider CPT, V-CPT, and CDMFT within a unified framework.In the CDMFT construction [2, 4] the infinite lattice is tiled with identical clusters of size N c . In an effective action description, the degrees of freedom in a single cluster are treated exactly, while the remainin...

Using variational cluster perturbation theory we study the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the t-t(')-t('')-U Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of dSC that should be observable in photoemission experiments.

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism and d-wave superconductivity in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the twodimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t ′ , the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t ′′ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc/T max c phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BardeenCooper-Schrieffer approach. At strong coupling, d-wave superconductivity and antiferromagnetism appear naturally as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.