Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model

For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.Comment: 32 pages, 12 figures, submtted to JSTA

Multi-band Gutzwiller wave functions for general on-site interactions

We introduce Gutzwiller wave functions for multi-band models with general on-site Coulomb interactions. As these wave functions employ correlators for the exact atomic eigenstates they are exact both in the non-interacting and in the atomic limit. We evaluate them in infinite lattice dimensions for all interaction strengths without any restrictions on the structure of the Hamiltonian or the symmetry of the ground state. The results for the ground-state energy allow us to derive an effective one-electron Hamiltonian for Landau quasi-particles, applicable for finite temperatures and frequencies within the Fermi-liquid regime. As applications for a two-band model we study the Brinkman-Rice metal-to-insulator transition at half band-filling, and the transition to itinerant ferromagnetism for two specific fillings, at and close to a peak in the density of states of the non-interacting system. Our new results significantly differ from those for earlier Gutzwiller wave functions where only density-type interactions were included. When the correct spin symmetries for the two-electron states are taken into account, the importance of the Hund's-rule exchange interaction is even more pronounced and leads to paramagnetic metallic ground states with large local magnetic moments. Ferromagnetism requires fairly large interaction strengths, and the resulting ferromagnetic state is a strongly correlated metal.Comment: 37 pages, 10 figures; accepted for publication in Phys. Rev. B 57 (March 15, 1998

Optical conductivity of the half-filled Hubbard chain

We combine well-controlled analytical and numerical methods to determine the optical conductivity of the one-dimensional Mott-Hubbard insulator at zero temperature. A dynamical density-matrix renormalization group method provides the entire absorption spectrum for all but very small coupling strengths. In this limit we calculate the conductivity analytically using exact field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another weak feature becomes visible around the middle of the absorption band.Comment: 4 pages with 3 eps figures, published version (changes in text and references

Random phase approximation for multi-band Hubbard models

We derive the random-phase approximation for spin excitations in general multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock ground state. The results are compared with those of a recently introduced variational many-body approach to spin-waves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the Hartree-Fock theory fails to describe properly the local moments which naturally arise in a correlated-electron theory.Comment: 25 pages, 2 figure

Effects of the Nearest-Neighbour Coulomb Interactions on the Ground State of the Periodic Anderson Model

The magnetic and non-magnetic ground states of the periodic Anderson model with Coulomb interaction between $f$-electrons on the nearest-neighbour(NN) sites are investigated using a variational method, which gives exact calculation of the expectation values in the limit of infinite dimensions. It is shown that for a critical value of NN Coulomb interactions the magnetic ground state of the periodic Anderson model in the Kondo regime is unstable. Factors in terms of the physical processes responsible for instability of the magnetic ground state are also discussed. Our study indicates the importance of the NN Coulomb interactions for correlated two band models.Comment: RevTeX, 6 pages, 5 figures, to appear in Phys. Rev.

Humanitarian aid as an integral part of the European Union's external action: the challenge of reconciling coherence and independence

The article focuses on the European Union's (EU) humanitarian aid policy. It addresses the challenge for the EU to deliver independent humanitarian aid while simultaneously seeking to establish more coherence between its external policies. The article examines how the EU tries to reconcile these potentially conflicting policy goals, both de jure and in practice. Empirically, it explores the interaction between EU humanitarian aid and development cooperation, the Common Foreign and Security Policy, and trade policy. While the independence of the humanitarian aid delivery is, for the most part, not being undermined, it remains difficult to establish positive synergies with other external policies because of institutional hurdles and legal constraints, as well as political obstacles and operational incompatibilities

Modulation spectroscopy with ultracold fermions in an optical lattice

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time dependent density-matrix renormalization group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott-insulator, respectively. In the Mott-insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations

Photoemission study of (V1−x_{1-x}Mx_x)2_2O3_3 (M=Cr, Ti)

We present high-resolution bulk-sensitive photoemission spectra of (V$_{1-x}$M$_x$)$_2$O$_3$ (M=Cr, Ti). The measurements were made for the paramagnetic metal (PM), paramagnetic insulator (PI), and antiferromagnetic insulator (AFI) phases of (V$_{1-x}$M$_x$)$_2$O$_3$ with the samples of $x$ = 0, 0.012, and 0.028 for Cr-doping and $x$ = 0.01 for Ti-doping. In the PM phase, we observe a prominent quasiparticle peak in general agreement with theory, which combines dynamical mean-field theory with the local density approximation (LDA+DMFT). The quasiparticle peak shows a significantly larger peak width and weight than in the theory. For both the PI and AFI phases, the vanadium 3d parts of the valence spectra are not simple one peak structures. For the PI phase, there is not yet a good theoretical understanding of these structures. The size of the electron removal gap increases, and spectral weight accumulates in the energy range closer to the chemical potential, when the PI to AFI transition occurs. Spectra taken in the same phases with different compositions show interesting monotonic changes as the dopant concentration increases, regardless of the dopant species. With increased Cr-doping, the AFI phase gap decreases and the PI phase gap increases.Comment: 13 pages, 16 figures. accepted for publication in Physical Review

Exact Solution of the strong coupling t-V model with twisted boundary conditions

We present the solution of the one-dimensional t-V model with twisted boundary conditions in the strong coupling limit, t<<V and show that this model can be mapped onto the strong coupling Hubbard chain threaded by a fictitious flux proportional to the total momentum of the charge carriers. The high energy eigenstates are characterized by a factorization of degrees of freedom associated with configurations of soliton and antisoliton domains and degrees of freedom associated with the movement of ``holes'' through these domains. The coexistence of solitons and antisolitons leads to a strange flux dependence of the eigenvalues. We illustrate the use of this solution, deriving the full frequency dependence of the optical conductivity at half-filling and zero temperature.Comment: 11 pages, 1 figure; to be published in Physical Review

Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model

We present a symmetry-projected configuration mixing scheme to describe ground and excited states, with well defined quantum numbers, of the two-dimensional Hubbard model with nearestneighbor hopping and periodic boundary conditions. Results for the half-filled 2{\times}4, 4{\times}4, and 6{\times}6 lattices, as well as doped 4 {\times} 4 systems, compare well with available results, both exact and from other state-of-the-art approximations. We report spectral functions and density of states obtained from a well-controlled ansatz for the (Ne {\pm} 1)-electron system. Symmetry projected methods have been widely used for the many-body nuclear physics problem but have received little attention in the solid state community. Given their relatively low (mean-field) computational cost and the high quality of results here reported, we believe that they deserve further scrutiny