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

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

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

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

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

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

Dynamical mean-field theory of indirect magnetic exchange

To analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces, the real-space extension of dynamical mean-field theory (R-DMFT) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity. While R-DMFT describes the Kondo effect of a single adatom exactly, indirect magnetic (RKKY) exchange is taken into account on an approximate level only. Here, we consider a simplified model system consisting of two magnetic Hubbard sites ("adatoms") hybridizing with a non-interacting tight-binding chain ("substrate surface"). This two-impurity Anderson model incorporates the competition between the Kondo effect and indirect exchange but is amenable to an exact numerical solution via the density-matrix renormalization group (DMRG). The particle-hole symmetric model at half-filling and zero temperature is used to benchmark R-DMFT results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate. In particular, the dependence of the local adatom and the nonlocal adatom-adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied. We find both, excellent agreement with the DMRG data even on subtle details of the competition between RKKY exchange and the Kondo effect but also complete failure of the R-DMFT, depending on the parameter regime considered. R-DMFT calculations are performed using the Lanczos method as impurity solver. With the real-space extension of the two-site DMFT, we also benchmark a simplified R-DMFT variant.Comment: 14 pages, 8 figure

Variational Cluster Perturbation Theory for Bose-Hubbard models

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator--to--superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum -- free of spurious gaps -- despite the fact that if formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimension dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.Comment: v1) 10 pages, 6 figures. v2) Final version as publishe

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation also extends the known nonequilibrium moment sum rules for the Green's functions to the third moment). These sum rules are used to further test the accuracy of nonequilibrium solutions to the many-body problem; for example, we illustrate how well the self-energy sum rules are satisfied for the Falicov-Kimball model in infinite dimensions and placed in a uniform electric field turned on at time t=0. In general, the self-energy sum rules are satisfied to a significantly higher accuracy than the Green's functions sum rules

Phase diagram of orbital-selective Mott transitions at finite temperatures

Mott transitions in the two-orbital Hubbard model with different bandwidths are investigated at finite temperatures. By means of the self-energy functional approach, we discuss the stability of the intermediate phase with one orbital localized and the other itinerant, which is caused by the orbital-selective Mott transition (OSMT). It is shown that the OSMT realizes two different coexistence regions at finite temperatures in accordance with the recent results of Liebsch. We further find that the particularly interesting behavior emerges around the special condition $U=U'$ and J=0, which includes a new type of the coexistence region with three distinct states. By systematically changing the Hund coupling, we establish the global phase diagram to elucidate the key role played by the Hund coupling on the Mott transitions.Comment: 4 pages, 6 figure