Correlation and surface effects in Vanadium Oxides

Recent photoemission experiments have shown strong surface modifications in the spectra from vanadium oxides as (V,Cr)_2O_3 or (Sr,Ca)VO_3. The effective mass is enhanced at the surface and the coherent part of the surface spectrum is narrowed as compared to the bulk. The quasiparticle weight is more sensitive at the surface than in the bulk against bandwidth variations. We investigate these effects theoretically considering the single-band Hubbard model for a film geometry. A simplified dynamical mean-field scheme is used to calculate the main features of the interacting layer-dependent spectral function. It turns out that the experimentally confirmed effects are inherent properties of a system of strongly correlated electrons. The reduction of the weight and the variance of the coherent part of the surface spectrum can be traced back to the reduced surface coordination number. Surface correlation effects can be strongly amplified by changes of the hopping integrals at the surface.Comment: to appear in PRB; 8 pages, 6 figure

Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio

Zero-temperature Phase Diagram of Two Dimensional Hubbard Model

We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with $(\pi, \pi)$ and $(2\pi/3, 2\pi/3)$ structures. It is shown that a non-magnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with $(2\pi/3, 2\pi/3)$ structure.Comment: 4 pages, 4 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

Two-site dynamical mean-field theory

It is shown that a minimum realization of the dynamical mean-field theory (DMFT) can be achieved by mapping a correlated lattice model onto an impurity model in which the impurity is coupled to an uncorrelated bath that consists of a single site only. The two-site impurity model can be solved exactly. The mapping is approximate. The self-consistency conditions are constructed in a way that the resulting ``two-site DMFT'' reduces to the previously discussed linearized DMFT for the Mott transition. It is demonstrated that a reasonable description of the mean-field physics is possible with a minimum computational effort. This qualifies the simple two-site DMFT for a systematic study of more complex lattice models which cannot be treated by the full DMFT in a feasible way. To show the strengths and limitations of the new approach, the single-band Hubbard model is investigated in detail. The predictions of the two-site DMFT are compared with results of the full DMFT. Internal consistency checks are performed which concern the Luttinger sum rule, other Fermi-liquid relations and thermodynamic consistency.Comment: LaTeX, 14 pages, 8 eps figures included, Phys. Rev. B (in press

Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects

Using the variational cluster approach (VCA), we study the transition from the antiferromagnetic to the superconducting phase of the two-dimensional Hubbard model at zero temperature. Our calculations are based on a new method to evaluate the VCA grand potential which employs a modified Lanczos algorithm and avoids integrations over the real or imaginary frequency axis. Thereby, very accurate results are possible for cluster sizes not accessible to full diagonalization. This is important for an improved treatment of short-range correlations, including correlations between Cooper pairs in particular. We investigate the cluster-size dependence of the phase-separation tendency that has been proposed recently on the basis of calculations for smaller clusters. It is shown that the energy barrier driving the phase separation decreases with increasing cluster size. This supports the conjecture that the ground state exhibits microscopic inhomogeneities rather than macroscopic phase separation. The evolution of the single-particle spectum as a function of doping is studied in addtion and the relevance of our results for experimental findings is pointed out.Comment: 7 pages, 6 figures, published versio

Surface metal-insulator transition in the Hubbard model

The correlation-driven metal-insulator (Mott) transition at a solid surface is studied within the Hubbard model for a semi-infinite lattice by means of the dynamical mean-field theory. The transition takes place at a unique critical strength of the interaction. Depending on the surface geometry, the interaction strength and the wave vector, we find one-electron excitations in the coherent part of the surface-projected metallic spectrum which are confined to two dimensions.Comment: LaTeX, 9 pages, 5 eps figures included, Phys. Rev. B (in press

Competition between Kondo screening and indirect magnetic exchange in a quantum box

Nanoscale systems of metal atoms antiferromagnetically exchange coupled to several magnetic impurities are shown to exhibit an unconventional re-entrant competition between Kondo screening and indirect magnetic exchange interaction. Depending on the atomic positions of the magnetic moments, the total ground-state spin deviates from predictions of standard Ruderman-Kittel-Kasuya-Yosida perturbation theory. The effect shows up on an energy scale larger than the level width induced by the coupling to the environment and is experimentally verifiable by studying magnetic field dependencies.Comment: 5 pages, 2 figures, v3 with minor change

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

Mott transitions in correlated electron systems with orbital degrees of freedom

Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction U_c for any integer filling n and different M at zero temperature. For half-filling a linear dependence of U_c on M is found. Inclusion of the (full) Hund's rule exchange J results in a strong reduction of U_c. The transition turns out to change qualitatively from continuous for J=0 to discontinuous for any finite J