Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory

This 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 has 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 approximation), and Cellular Dynamical Mean-Field Theory.Comment: 32 pages, 51 figures. Slight modifications to text, figures and references. A PDF file with higher-resolution figures is available at http://www.physique.usherbrooke.ca/senechal/LTP-toc.pd

Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films

The influence of uncorrelated (nonmagnetic) overlayers on the magnetic properties of thin itinerant-electron films is investigated within the single-band Hubbard model. The Coulomb correlation between the electrons in the ferromagnetic layers is treated by using the spectral density approach (SDA). It is found that the presence of nonmagnetic layers has a strong effect on the magnetic properties of thin films. The Curie temperatures of very thin films are modified by the uncorrelated overlayers. The quasiparticle density of states is used to analyze the results. In addition, the coupling between the ferromagnetic layers and the nonmagnetic layers is discussed in detail. The coupling depends on the band occupation of the nonmagnetic layers, while it is almost independent of the number of the nonmagnetic layers. The induced polarization in the nonmagnetic layers shows a long-range decreasing oscillatory behavior and it depends on the coupling between ferromagnetic and nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see: http://orion.physik.hu-berlin.d

Charge ordering in extended Hubbard models: Variational cluster approach

We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalisation of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions U>=3t. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.Comment: 15 pages, 12 figure

Theory of Spin-Resolved Auger-Electron Spectroscopy from Ferromagnetic 3d-Transition Metals

CVV Auger electron spectra are calculated for a multi-band Hubbard model including correlations among the valence electrons as well as correlations between core and valence electrons. The interest is focused on the ferromagnetic 3d-transition metals. The Auger line shape is calculated from a three-particle Green function. A realistic one-particle input is taken from tight-binding band-structure calculations. Within a diagrammatic approach we can distinguish between the \textit{direct} correlations among those electrons participating in the Auger process and the \textit{indirect} correlations in the rest system. The indirect correlations are treated within second-order perturbation theory for the self-energy. The direct correlations are treated using the valence-valence ladder approximation and the first-order perturbation theory with respect to valence-valence and core-valence interactions. The theory is evaluated numerically for ferromagnetic Ni. We discuss the spin-resolved quasi-particle band structure and the Auger spectra and investigate the influence of the core hole.Comment: LaTeX, 12 pages, 8 eps figures included, Phys. Rev. B (in press

Interacting and Annealing Particle Filters: Mathematics and a Recipe for Applications

Interacting and annealing are two powerful strategies that are applied in different areas of stochastic modelling and data analysis. Interacting particle systems approximate a distribution of interest by a finite number of particles where the particles interact between the time steps. In computer vision, they are commonly known as particle filters. Simulated annealing, on the other hand, is a global optimization method derived from statistical mechanics. A recent heuristic approach to fuse these two techniques for motion capturing has become known as annealed particle filter. In order to analyze these techniques, we rigorously derive in this paper two algorithms with annealing properties based on the mathematical theory of interacting particle systems. Convergence results and sufficient parameter restrictions enable us to point out limitations of the annealed particle filter. Moreover, we evaluate the impact of the parameters on the performance in various experiments, including the tracking of articulated bodies from noisy measurements. Our results provide a general guidance on suitable parameter choices for different applications

Temperature-dependent electronic structure and ferromagnetism in the d=oo Hubbard model studied by a modfied perturbation theory

The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the dispersions and the weights of the Hubbard bands in the strong-coupling regime for arbitrary fillings. Results are presented for the hyper-cubic and an fcc-type lattice. For the latter we find ferromagnetic solutions. The filling-dependent Curie temperature is compared with the results of a recent Quantum Monte Carlo study.Comment: RevTeX, 5 pages, 6 eps figures included, Phys. Rev. B (in press), Ref. 16 correcte

Ferromagnetism and Temperature-Driven Reorientation Transition in Thin Itinerant-Electron Films

The temperature-driven reorientation transition which, up to now, has been studied by use of Heisenberg-type models only, is investigated within an itinerant-electron model. We consider the Hubbard model for a thin fcc(100) film together with the dipole interaction and a layer-dependent anisotropy field. The isotropic part of the model is treated by use of a generalization of the spectral-density approach to the film geometry. The magnetic properties of the film are investigated as a function of temperature and film thickness and are analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the temperature dependence of the second-order anisotropy constants we find that both types of reorientation transitions, from out-of-plane to in-plane (``Fe-type'') and from in-plane to out-of-plane (``Ni-type'') magnetization are possible within our model. In the latter case the inclusion of a positive volume anisotropy is vital. The reorientation transition is mediated by a strong reduction of the surface magnetization with respect to the inner layers as a function of temperature and is found to depend significantly on the total band occupation.Comment: 10 pages, 8 figures included (eps), Phys Rev B in pres

Three-point correlations for quantum star graphs

We compute the three point correlation function for the eigenvalues of the Laplacian on quantum star graphs in the limit where the number of edges tends to infinity. This extends a work by Berkolaiko and Keating, where they get the 2-point correlation function and show that it follows neither Poisson, nor random matrix statistics. It makes use of the trace formula and combinatorial analysis.Comment: 10 pages, 2 figure