arXiv subjects

F. Gebhard

Publications and source records attributed to F. Gebhard.

At least 37 records · Page 2Linked to original sources

arXiv2008

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $L\leq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{\rm c}\approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.

cond-mat.str-el↗

arXiv2008

Hopping conduction in strong electric fields: Negative differential conductivity

Effects of strong electric fields on hopping conductivity are studied theoretically. Monte-Carlo computer simulations show that the analytical theory of Nguyen and Shklovskii [Solid State Commun. 38, 99 (1981)] provides an accurate description of hopping transport in the limit of very high electric fields and low concentrations of charge carriers as compared to the concentration of localization sites and also at the relative concentration of carriers equal to 0.5. At intermediate concentrations of carriers between 0.1 and 0.5 computer simulations evidence essential deviations from the results of the existing analytical theories. The theory of Nguyen and Shklovskii also predicts a negative differential hopping conductivity at high electric fields. Our numerical calculations confirm this prediction qualitatively. However the field dependence of the drift velocity of charge carriers obtained numerically differs essentially from the one predicted so far. Analytical theory is further developed so that its agreement with numerical results is essentially improved.

cond-mat.dis-nn↗

arXiv2008

Phase diagram of the t-U-J1-J2 chain at half filling

We investigate the half-filled Hubbard chain with additional nearest- and next-nearest-neighbor spin exchange, J1 and J2, using bosonization and the density-matrix renormalization group. For J2 = 0 we find a spin-density-wave phase for all positive values of the Hubbard interaction U and the Heisenberg exchange J1. A frustrating spin exchange J2 induces a bond-order-wave phase. For some values of J1, J2 and U, we observe a spin-gapped metallic Luther-Emery phase.

cond-mat.str-el↗

arXiv2008

Effective temperature for hopping transport in a Gaussian DOS

For hopping transport in disordered materials, the mobility of charge carriers is strongly dependent on temperature and the electric field. Our numerical study shows that both the energy distribution and the mobility of charge carriers in systems with a Gaussian density of states, such as organic disordered semiconductors, can be described by a single parameter - effective temperature, dependent on the magnitude of the electric field. Furthermore, this effective temperature does not depend on the concentration of charge carriers, while the mobility does depend on the charge carrier concentration. The concept of the effective temperature is shown to be valid for systems with and without space-energy correlations in the distribution of localized states.

cond-mat.dis-nn↗

arXiv2008

Spin-orbit coupling in ferromagnetic Nickel

We use the Gutzwiller variational theory to investigate the electronic and the magnetic properties of fcc-Nickel. Our particular focus is on the effects of the spin-orbit coupling. Unlike standard relativistic band-structure theories, we reproduce the experimental magnetic moment direction and we explain the change of the Fermi-surface topology that occurs when the magnetic moment direction is rotated by an external magnetic field. The Fermi surface in our calculation deviates from early de-Haas--van-Alphen (dHvA) results. We attribute these discrepancies to an incorrect interpretation of the raw dHvA data.

cond-mat.str-el↗

arXiv2008

Spin-dependent transition rates through exchange coupled localized spin pairs during coherent spin excitation

The effect of exchange interactions within spin pairs on spin-dependent transport and recombination rates through localized states in semiconductors during coherent electron spin resonant excitation is studied theoretically. It is shown that for identical spin systems, significant quantitative differences are to be expected between the results of pEDMR/pODMR experiments were permutation symmetry is the observable as compared to pESR experiments with polarization as the observable. It is predicted that beat oscillations of the spin nutations and not the nutations themselves dominate the transport or recombination rates when the exchange coupling strength or the field strength of the exciting radiation exceed the difference of the Zeeman energies within the spin pair. Furthermore, while the intensities of the rate oscillations decrease with increasing exchange within the spin pairs, the singlet and triplet signals retain their relative strength. This means that pEDMR and pODMR experiments could allow better experimental access to ESR forbidden singlet transitions which are hardly or not at all accessible with conventional pulsed electron spin resonance spectroscopy.

cond-mat.mtrl-sci↗

arXiv2006

Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal-insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott-Hubbard transition in the limit of infinite dimensions.

cond-mat.str-el↗

arXiv2005

Optical excitations of Peierls-Mott insulators with bond disorder

The density-matrix renormalization group (DMRG) is employed to calculate optical properties of the half-filled Hubbard model with nearest-neighbor interactions. In order to model the optical excitations of oligoenes, a Peierls dimerization is included whose strength for the single bonds may fluctuate. Systems with up to 100 electrons are investigated, their wave functions are analyzed, and relevant length-scales for the low-lying optical excitations are identified. The presented approach provides a concise picture for the size dependence of the optical absorption in oligoenes.

cond-mat.str-el↗

arXiv2004

Spectral function of the one-dimensional Hubbard model away from half filling

We calculate the photoemission spectral function of the one-dimensional Hubbard model away from half filling using the dynamical density matrix renormalization group method. An approach for calculating momentum-dependent quantities in finite open chains is presented. Comparison with exact Bethe Ansatz results demonstrates the unprecedented accuracy of our method. Our results show that the photoemission spectrum of the quasi-one-dimensional conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of the conduction band width.

cond-mat.str-el↗

arXiv2003

Landau-Gutzwiller quasi-particles

We define Landau quasi-particles within the Gutzwiller variational theory, and derive their dispersion relation for general multi-band Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were based on a phenomenological effective single-particle Hamiltonian. For the one-band Hubbard model we calculate the first-order corrections in 1/D and find that the corrections to the quasi-particle dispersions are small in three dimensions. They may be largely absorbed in a rescaling of the total band width, unless the system is close to half band filling. Therefore, the Gutzwiller theory in the limit of large dimensions provides quasi-particle bands which are suitable for a comparison with real, three-dimensional Fermi liquids.

cond-mat.str-el↗

arXiv2002

Atomic correlations in itinerant ferromagnets: quasi-particle bands of nickel

We measure the band structure of nickel along various high-symmetry lines of the bulk Brillouin zone with angle-resolved photoelectron spectroscopy. The Gutzwiller theory for a nine-band Hubbard model whose tight-binding parameters are obtained from non-magnetic density-functional theory resolves most of the long-standing discrepancies between experiment and theory on nickel. Thereby we support the view of itinerant ferromagnetism as induced by atomic correlations.

cond-mat.str-el↗

arXiv2001

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.

cond-mat.str-el↗

arXiv2001

On the way to a Gutzwiller density functional theory

Multi-band Gutzwiller-correlated wave functions reconcile the contrasting concepts of itinerant band electrons versus electrons localized in partially filled atomic shells. The exact evaluation of these variational ground states in the limit of large coordination number allows the identification of quasi-particle band structures, and the calculation of a variational spinwave dispersion. The study of a generic two-band model elucidates the co-operation of the Coulomb repulsion and the Hund's-rule exchange for itinerant ferromagnetism. We present results of calculations for ferromagnetic nickel, using a realistic 18 spin-orbital basis of $4s$, $4p$ and $3d$ valence electrons. The quasi-particle energy bands agree much better with the photo-emission and Fermi surface data than the band structure obtained from spin-density functional theory (SDFT).

cond-mat.str-el↗

arXiv2001

Excitons in one-dimensional Mott insulators

We employ dynamical density-matrix renormalization group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of `small' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (`holon-antiholon' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.

cond-mat.str-el↗

arXiv2000

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.

cond-mat.str-el↗

arXiv1999

Mott-Hubbard transition in infinite dimensions

We calculate the zero-temperature gap and quasiparticle weight of the half-filled Hubbard model with a random dispersion relation. After extrapolation to the thermodynamic limit, we obtain reliable bounds on these quantities for the Hubbard model in infinite dimensions. Our data indicate that the Mott-Hubbard transition is continuous, i.e., that the quasiparticle weight becomes zero at the same critical interaction strength at which the gap opens.

cond-mat.str-el↗

arXiv1997

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.

cond-mat.str-el↗

arXiv1996

Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $δ$. New correction (``$η$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $Wδ< ω< W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.

cond-mat↗