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We calculate the spectral weight of the one- and two-dimensional Hubbard models by performing exact diagonalizations of finite clusters and treating intercluster hopping with perturbation theory. Even with relatively modest clusters (e.g., 12 sites), the spectra thus obtained give an accurate description of the exact results. Spin-charge separation (i.e., an extended spectral weight bounded by singularities dispersing with wave vector) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.

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...

Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strongcoupling perturbation theory at leading order. It is exact in both the strong-and weak-coupling limits and provides a good approximation to the spectral function at any wavevector. Following the paper by Sénéchal et al. (Phys. Rev. Lett. 84, 522 (2000)), we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the t − t ′ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.

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.

Using cluster perturbation theory, it is shown that the spectral weight and pseudogap observed at the Fermi energy in recent angle resolved photoemission spectroscopy of both electron- and hole-doped high-temperature superconductors find their natural explanation within the t-t(')-t(")-U Hubbard model in two dimensions. The value of the interaction U needed to explain the experiments for electron-doped systems at optimal doping is in the weak to intermediate coupling regime where the t-J model is inappropriate. At strong coupling, short-range correlations suffice to create a pseudogap, but at weak-coupling long correlation lengths associated with the antiferromagnetic wave vector are necessary.

Articles you may be interested inIron-based superconductors: Magnetism, superconductivity, and electronic structure (Review Article) Low Temp. Phys. 38, 888 (2012); 10.1063/1.4752092 Applying BCS-BEC crossover theory to high-temperature superconductors and ultracold atomic Fermi gases (Review Article) Low Temp. ͑Submitted November 2, 2005͒ Fiz. Nizk. Temp. 32, 561-595͑April-May 2006͒This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole-and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the two-particle self-consistent approach, variational cluster perturbation theory ͑or variational cluster approximation͒, and cellular dynamical mean-field theory.