arXiv subjects

D. Vollhardt

Publications and source records attributed to D. Vollhardt.

At least 73 records · Page 4Linked to original sources

arXiv2001

On the Analyticity of Solutions in the Dynamical Mean-Field Theory

The unphysical solutions of the periodic Anderson model obtained by H. Keiter and T. Leuders [Europhys. Lett. 49, 801(2000)] in dynamical mean-field theory (DMFT) are shown to result from the author's restricted choice of the functional form of the solution, leading to a violation of the analytic properties of the exact solution. By contrast, iterative solutions of the self-consistency condition within the DMFT obtained by techniques which preserve the correct analytic properties of the exact solution (e.g., quantum Monte-Carlo simulations or the numerical renormalization group) always lead to physical solutions.

cond-mat.str-el↗

arXiv2001

Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism

We study the Hubbard model with bond-charge interaction (`correlated hopping') in terms of the Gutzwiller wave function. We show how to express the Gutzwiller expectation value of the bond-charge interaction in terms of the correlated momentum-space occupation. This relation is valid in all spatial dimensions. We find that in infinite dimensions, where the Gutzwiller approximation becomes exact, the bond-charge interaction lowers the critical Hubbard interaction for the Brinkman-Rice metal-insulator transition. The bond-charge interaction also favors ferromagnetic transitions, especially if the density of states is not symmetric and has a large spectral weight below the Fermi energy.

cond-mat.str-el↗

arXiv2000

Finite temperature numerical renormalization group study of the Mott-transition

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T T_c there is a smooth crossover from metallic-like to insulating-like solutions.

cond-mat.str-el↗

arXiv2000

Metallic Ferromagnetism - an Electronic Correlation Phenomenon

New insights into the microscopic origin of itinerant ferromagnetism were recently gained from investigations of electronic lattice models within dynamical mean-field theory (DMFT). In particular, it is now established that even in the one-band Hubbard model metallic ferromagnetism is stable at intermediate values of the interaction U and density n on regular, frustrated lattices. Furthermore, band degeneracy along with Hund's rule couplings is very effective in stabilizing metallic ferromagnetism in a broad range of electron fillings. DMFT also permits one to investigate more complicated correlation models, e.g., the ferromagnetic Kondo lattice model with Coulomb interaction, describing electrons in manganites with perovskite structure. Here we review recent results obtained with DMFT which help to clarify the origin of band-ferromagnetism as a correlation phenomenon.

cond-mat.str-el↗

arXiv2000

Superfluid Helium 3: Link between Condensed Matter Physics and Particle Physics

The discovery of the superfluid phases of Helium 3 in 1971 opened the door to one of the most fascinating systems known in condensed matter physics. Superfluidity of Helium 3, originating from pair condensation of Helium 3 atoms, turned out to be the ideal testground for many fundamental concepts of modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and their spontaneous breakdown, topological defects, etc. Thereby the superfluid phases of Helium 3 enriched condensed matter physics enormously. In particular, they contributed significantly - and continue to do so - to our understanding of various other physical systems, from heavy fermion and high-Tc superconductors all the way to neutron stars, particle physics, gravity and the early universe. A simple introduction into the basic concepts and questions is presented.

cond-mat↗

arXiv2000

Mott-Hubbard Metal-Insulator Transition in Paramagnetic V_2O_3: a LDA+DMFT(QMC) Study

The electronic properties of paramagnetic V_2O_3 are investigated by the ab-initio computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses numerically exact quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V_2O_3 and insulating (V_{0.962}Cr_{0.038})_2O_3 we find a Mott-Hubbard metal-insulator-like transition at a Coulomb interaction U\approx 5eV. The calculated spectrum is in very good agreement with experiment. Furthermore, the occupation of the (a_{1g},e_{g1}^π,e_{g2}^π) orbitals and the spin state S=1 determined by us agree with recent polarization dependent X-ray-absorption experiments.

cond-mat.str-el↗

arXiv2000

Realistic modeling of strongly correlated electron systems: An introduction to the LDA+DMFT approach

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La_{1-x}Sr_xTiO_3, obtained by solving the DMFT-equations by quantum Monte-Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e., the iterative perturbation theory and the non-crossing approximation.

cond-mat.str-el↗

arXiv2000

Conductivity of disordered electrons: Mean-field approximation containing vertex corrections

The electrical {\em dc}-conductivity of disordered, non-interacting electrons is calculated in the asymptotic limit of high lattice dimensions $d\to \infty$. To go beyond the lowest-order contribution in the expansion parameter $1/d$ of the single bubble diagram, vertex corrections are calculated from an asymptotic expression for the two-particle vertex. A mean-field approximation for the dc-conductivity containing the leading high-dimensional vertex corrections is proposed which is free of spurious non-analyticities, i.e. the conductivity is non-negative and shows no unphysical behavior in $d\geq 3$.

cond-mat.str-el↗

arXiv2000

Calculation of photoemission spectra of the doped Mott insulator La_{1-x}Sr_xTiO_3 using LDA+DMFT(QMC)

The spectral properties of La$_{1-x}$Sr$_{x}$TiO$_{3}$, a doped Mott insulator with strong Coulomb correlations, are calculated with the ab initio computational scheme LDA+DMFT(QMC). It starts from the non-interacting electronic band structure as calculated by the local density approximation (LDA), and introduces the missing correlations by the dynamical mean-field theory (DMFT), using numerically exact quantum Monte-Carlo (QMC) techniques to solve the resulting self-consistent multi-band single-impurity problem. The results of the LDA+DMFT(QMC) approach for the photoemission spectra of La$_{1-x}$Sr$_{x}$TiO$_{3}$ are in good agreement with experiment and represent a considerable qualitative and quantitative improvement on standard LDA calculations.

cond-mat.str-el↗

arXiv2000

Anderson impurity in a correlated conduction band

We investigate the physics of a magnetic impurity with spin 1/2 in a correlated metallic host. Describing the band by a Hubbard Hamiltonian, the problem is analyzed using dynamical mean-field-theory in combination with Wilson's nonperturbative numerical renormalization group. We present results for the single-particle density of states and the dynamical spin susceptibility at zero temperature. New spectral features (side peaks) are found which should be observable experimentally. In addition, we find a general enhancement of the Kondo scale due to correlations. Nevertheless, in the metallic phase, the Kondo scale always vanishes exponentially in the limit of small hybridization.

cond-mat.str-el↗

arXiv2000

Electronic Correlations in Manganites

The influence of local electronic correlations on the properties of colossal magnetoresistance manganites is investigated. To this end, a ferromagnetic two-band Kondo lattice model is supplemented with the local Coulomb repulsion missing in this model, and is analyzed within dynamical mean-field theory. Results for the spectral function, optical conductivity, and the paramagnetic-to-ferromagnetic phase transition show that electronic correlations have drastic effects and may explain some experimental observations.

cond-mat.str-el↗

arXiv1999

Nearly universal crossing point of the specific heat curves of Hubbard models

A nearly universal feature of the specific heat curves C(T,U) vs. T for different U of a general class of Hubbard models is observed. That is, the value C_+ of the specific heat curves at their high-temperature crossing point T_+ is almost independent of lattice structure and spatial dimension d, with C_+/k_B \approx 0.34. This surprising feature is explained within second order perturbation theory in U by identifying two small parameters controlling the value of C_+: the integral over the deviation of the density of states N(ε) from a constant value, characterized by δN=\int dε|N(ε)-1/2|, and the inverse dimension, 1/d.

cond-mat.str-el↗

arXiv1999

Absence of hysteresis at the Mott-Hubbard metal-insulator transition in infinite dimensions

The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by Quantum Monte Carlo simulations down to temperature T=W/140 (W=bandwidth). Calculating with significantly higher precision than in previous work, we show that the hysteresis below T_{IPT}\simeq 0.022W, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least T=0.325T_{IPT}. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.

cond-mat.str-el↗

arXiv1998

Disorder and Impurities in Hubbard-Antiferromagnets

We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.

cond-mat.str-el↗

arXiv1998

Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions $d=1,$ 2, and $\infty$ on regular lattices and at intermediate values of the interaction $U$ and density $n$. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.

cond-mat.str-el↗

arXiv1998

Microscopic conditions favoring itinerant ferromagnetism

A systematic investigation of the microscopic conditions stabilizing itinerant ferromagnetism of correlated electrons in a single-band model is presented. Quantitative results are obtained by quantum Monte Carlo simulations for a model with Hubbard interaction U and direct Heisenberg exchange interaction F within the dynamical mean-field theory. Special emphasis is placed on the investigation of (i) the distribution of spectral weight in the density of states, (ii) the importance of genuine correlations, and (iii) the significance of the direct exchange, for the stability of itinerant ferromagnetism at finite temperatures. We find that already a moderately strong peak in the density of states near the band edge suffices to stabilize ferromagnetism at intermediate U-values in a broad range of electron densities n. Correlation effects prove to be essential: Slater--Hartree-Fock results for the transition temperature are both qualitatively and quantitatively incorrect. The nearest-neighbor Heisenberg exchange does not, in general, play a decisive role. Detailed results for the magnetic phase diagram as a function of U, F, n, temperature T, and the asymmetry of the density of states are presented and discussed.

cond-mat.str-el↗

arXiv1998

Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy

The importance of Hund's rule coupling for the stabilization of itinerant ferromagnetism is investigated within a two-band Hubbard model. The magnetic phase diagram is calculated by finite-temperature quantum Monte Carlo simulations within the dynamical mean-field theory. Ferromagnetism is found in a broad range of electron fillings whereas antiferromagnetism exists only near half filling. The possibility of orbital ordering at quarter filling is also analyzed.

cond-mat.str-el↗

arXiv1998

Frustration of antiferromagnetism in the t-t'-Hubbard model at weak coupling

The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t'. The exact asymptotic behavior of the critical coupling U_c(t') at small t' is calculated in dimensions d=2,3 and infinity using Hartree theory, and the order of the transition is determined. A region of stability of a metallic antiferromagnetic phase in d=3 is identified.

cond-mat.str-el↗