Dynamic response functions for the Holstein-Hubbard model

We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propagator shows a characteristic softening near the metal to bipolaronic transition but there is very little softening on the approach to the Mott transition.Comment: 13 pages, 19 figure

First- and Second Order Phase Transitions in the Holstein-Hubbard Model

We investigate metal-insulator transitions in the Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U. We also present results for the quasiparticle weight and the double-occupancy as function of U and g.Comment: 6 pages, 5 figure

Phase diagram and dynamic response functions of the Holstein-Hubbard model

We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half filling and at zero temperature. The calculations are based on the Dynamical Mean Field Theory. The effective impurity model is solved using Exact Diagonalization and the Numerical Renormalization Group. Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal insulator transitions.Comment: contribution to the SCES04 conferenc

Comment on "Fano Resonance for Anderson Impurity Systems"

In a recent Letter, Luo et al. (Phys. Rev. Lett. 92, 256602 (2004)) analyze the Fano line shapes obtained from scanning tunneling spectroscopy (STS) of transition metal impurities on a simple metal surface, in particular of the Ti/Au(111) and Ti/Ag(100) systems. As the key point of their analysis, they claim that there is not only a Fano interference effect between the impurity d-orbital and the conduction electron continuum, as derived in Ujsaghy et al. (Phys. Rev. Lett. 85, 2557 (2000)), but that the Kondo resonance in the d-electron spectral density has by itself a second Fano line shape, leading to the experimentally observed spectra. In the present note we point out that this analysis is conceptually incorrect. Therefore, the quantitative agreement of the fitted theoretical spectra with the experimental results is meaningless.Comment: 1 page, no figures. Accepted for publication in PRL; revised version uploaded on November 18th, 200

Non-Fermi liquid signatures in the Hubbard Model due to van Hove singularities

When a van-Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a non-analytic contribution. This invalidates basic assumptions of Fermi liquid theory and within perturbative treatments leads to a non-Fermi liquid self-energy and transport properties.Such anomalies are shown to also occur in the strongly correlated metallic state. We consider the Hubbard model on a two-dimensional square lattice with nearest and next-nearest neighbor hopping within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scale $T_0$ an unusual maximum emerges in the imaginary part of the self-energy which is renormalized towards the Fermi level for finite doping. At zero temperature this double-well structure is suppressed, but an anomalous energy dependence of the self-energy remains. For the frustrated Hubbard model on the square lattice with next-nearest neighbor hopping, the presence of the van Hove singularity changes the asymptotic low temperature behavior of the resistivity from a Fermi liquid to non-Fermi liquid dependency as function of doping. The results of this work are discussed regarding their relevance for high-temperature cuprate superconductors.Comment: revised version, accepted in Phys.Rev.

Imaginary-time formulation of steady-state nonequilibrium in quantum dot models

We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high order vertex corrections and its numerical analytic continuation procedures. The differential conductance calculations agree accurately with existing data from other nonequilibrium transport theories. It is verified that, at finite source-drain voltage, the Kondo resonance is destroyed at bias comparable to the Kondo temperature. Calculated coefficients in the scaling relation of the zero bias anomaly fall within the range of experimental estimates.Comment: 16 pages, 10 figures, Comparison to other theories adde

The Strong Coupling Fixed-Point Revisited

In recent work we have shown that the Fermi liquid aspects of the strong coupling fixed point of the s-d and Anderson models can brought out more clearly by interpreting the fixed point as a renormalized Anderson model, characterized by a renormalized level $\tilde\epsilon_d$, resonance width, $\tilde\Delta$, and interaction $\tilde U$, and a simple prescription for their calculation was given using the numerical renormalization group (NRG). These three parameters completely specify a renormalized perturbation theory (RPT) which leads to exact expressions for the low temperature behaviour. Using a combination of the two techniques, NRG to determine $\tilde\epsilon_d$, $\tilde\Delta$, and $\tilde U$, and then substituting these in the RPT expressions gives a very efficient and accurate way of calculating the low temperature behaviour of the impurity as it avoids the necessity of subtracting out the conduction electron component. Here we extend this approach to an Anderson model in a magnetic field, so that $\tilde\epsilon_d$, $\tilde\Delta$, and $\tilde U$ become dependent on the magnetic field. The de-renormalization of the renormalized quasiparticles can then be followed as the magnetic field strength is increased. Using these running coupling constants in a RPT calculation we derive an expression for the low temperature conductivity for arbitrary magnetic field strength.Comment: Contribution to JPSJ volume commemorating the 40th anniversary of the publication of Kondo's original pape

Thermopower of a Kondo-correlated quantum dot

The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model. Keywords: Thermoelectric and thermomagnetic effects, Coulomb blockade, single electron tunneling, Kondo-effect PACS Numbers: 72.20.Pa, 73.23.HkComment: 4 pages, 4 figures, revised version, changed figure

Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field

We derive an exact expression for the differential conductance for a quantum dot in an arbitrary magnetic field for small bias voltage. The derivation is based on the symmetric Anderson model using renormalized perturbation theory and is valid for all values of the on-site interaction $U$ including the Kondo regime. We calculate the critical magnetic field for the splitting of the Kondo resonance to be seen in the differential conductivity as function of bias voltage. Our calculations for small field show that the peak position of the component resonances in the differential conductance are reduced substantially from estimates using the equilibrium Green's function. We conclude that it is important to take the voltage dependence of the local retarded Green's function into account in interpreting experimental resultsComment: 8 pages, 4 figures; Replaced by a fully revised version with minor corrections in the tex

Quantum transport through a deformable molecular transistor

The linear transport properties of a model molecular transistor with electron-electron and electron-phonon interactions were investigated analytically and numerically. The model takes into account phonon modulation of the electronic energy levels and of the tunnelling barrier between the molecule and the electrodes. When both effects are present they lead to asymmetries in the dependence of the conductance on gate voltage. The Kondo effect is observed in the presence of electron-phonon interactions. There are important qualitative differences between the cases of weak and strong coupling. In the first case the standard Kondo effect driven by spin fluctuations occurs. In the second case, it is driven by charge fluctuations. The Fermi-liquid relation between the spectral density of the molecule and its charge is altered by electron-phonon interactions. Remarkably, the relation between the zero-temperature conductance and the charge remains unchanged. Therefore, there is perfect transmission in all regimes whenever the average number of electrons in the molecule is an odd integer.Comment: 9 pages, 6 figure