arXiv subjects

Florian Gebhard

Publications and source records attributed to Florian Gebhard.

51 records · Page 3Linked to original sources

arXiv2005

Tomonaga-Luttinger parameters for doped Mott insulators

The Tomonaga--Luttinger parameter $K_ρ$ determines the critical behavior in quasi one-dimensional correlated electron systems, e.g., the exponent $α$ for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate $K_ρ$ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine $K_ρ$ in the phase diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and confirm the bosonization results $K_ρ=n_{\rm c}^2=1/4$ on the critical line and $K_ρ^{\rm CDW}=n_{\rm c}^2/2=1/8$ at infinitesimal doping of the charge-density-wave (CDW) insulator for all interaction strengths. The doped CDW insulator exhibits exponents $α>1$ only for small doping and strong correlations.

cond-mat.str-el↗

arXiv2005

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.

cond-mat.str-el↗

arXiv2005

Gutzwiller-Correlated Wave Functions: Application to Ferromagnetic Nickel

Ferromagnetic Nickel is the most celebrated iron group metal with pronounced discrepancies between the experimental electronic properties and predictions of density functional theories. In this work, we show in detail that the recently developed multi-band Gutzwiller theory provides a very good description of the quasi-particle band structure of nickel. We obtain the correct exchange splittings and we reproduce the experimental Fermi-surface topology. The correct (111)-direction of the magnetic easy axis and the right order of magnitude of the magnetic anisotropy are found. Our theory also reproduces the experimentally observed change of the Fermi-surface topology when the magnetic moment is oriented along the (001)-axis. In addition to the numerical study, we give an analytical derivation for a much larger class of variational wave-functions than in previous investigations. In particular, we cover cases of superconductivity in multi-band lattice systems.

cond-mat.str-el↗

arXiv2005

Gutzwiller variational theory for the Hubbard model with attractive interaction

We investigate the electronic and superconducting properties of a negative-U Hubbard model. For this purpose we evaluate a recently introduced variational theory based on Gutzwiller-correlated BCS wave functions. We find significant differences between our approach and standard BCS theory, especially for the superconducting gap. For small values of $|U|$, we derive analytical expressions for the order parameter and the superconducting gap which we compare to exact results from perturbation theory.

cond-mat.str-el↗

arXiv2005

Macroscopic Aharonov--Bohm Effect in Type-I Superconductors

In type-I superconducting cylinders bulk superconductivity is destroyed above the first critical current. Below the second critical current the `type-I mixed state' displays fluctuation superconductivity which contributes to the total current. A magnetic flux on the axis of the cylinder can change the second critical current by as much as 50 percent so that half a flux quantum can switch the cylinder from normal conduction to superconductivity: the Aharonov--Bohm effect manifests itself in macroscopically large resistance changes of the cylinder.

cond-mat.supr-con↗

arXiv2005

Phase Diagram of the $t$--$U$--$V_1$--$V_2$ Model at Quarter Filling

We examine the ground-state properties of the one-dimensional Hubbard model at quarter filling with Coulomb interactions between nearest-neighbors $V_1$ and next-nearest neighbors $V_2$. Using the density-matrix renormalization group and exact diagonalization methods, we obtain an accurate ground-state phase diagram in the $V_1$-$V_2$ plane with three different phases: $2k_{\rm F}$- and $4k_{\rm F}$-charge-density-wave and a broad metallic phase in-between. The metal is a Tomonaga-Luttinger-liquid whose critical exponent $K_ρ$ is largest around $V_1=2V_2$, where $V_1$ and $V_2$ are frustrated, and smallest, $K_ρ=0.25$, at the boundaries between the metallic phase and each of the two ordered phases.

cond-mat.str-el↗

arXiv2004

Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at $U_{\rm c}$.

cond-mat.str-el↗

arXiv2003

Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization' scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at $U_{\rm c}=4.43 \pm 0.05$. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent $α=1/2$ in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott--Hubbard insulator.

cond-mat.str-el↗

arXiv2003

Fourth-Order Perturbation Theory for the Half-Filled Hubbard Model in Infinite Dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.

cond-mat.str-el↗

arXiv2001

Application of the Density Matrix Renormalization Group in momentum space

We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak to moderate interaction strength. In the one-dimensional models at half-filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.

cond-mat.str-el↗

arXiv2001

Mott-Hubbard Insulator in Infinite Dimensions

We calculate the one-particle density of states for the Mott-Hubbard insulating phase of the Hubbard model on a Bethe lattice in the limit of infinite coordination number. We employ the Kato-Takahashi perturbation theory around the strong-coupling limit to derive the Green function. We show that the Green function for the lower Hubbard band can be expressed in terms of polynomials in the bare hole-hopping operator. We check our technique against the exact solution of the Falicov-Kimball model and give explicit results up to and including second order in the inverse Hubbard interaction. Our results provide a stringent test for analytical and numerical investigations of the Mott-Hubbard insulator and the Mott-Hubbard transition within the dynamical mean-field theory. We find that the Hubbard-III approximation is not satisfactory beyond lowest order, but the local-moment approach provides a very good description of the Mott-Hubbard insulator at strong coupling.

cond-mat.str-el↗

arXiv2001

Excited States of Ladder-type Poly-p-phenylene Oligomers

Ground state properties and excited states of ladder-type paraphenylene oligomers are calculated applying semiempirical methods for up to eleven phenylene rings. The results are in qualitative agreement with experimental data. A new scheme to interpret the excited states is developed which reveals the excitonic nature of the excited states. The electron-hole pair of the S1-state has a mean distance of approximately 4 Angstroem.

cond-mat↗

arXiv2000

Multi-band Gutzwiller wave functions for itinerant ferromagnetism

Multi-band Gutzwiller-correlated wave functions reconcile the contrasting concepts of itinerant band electrons versus electrons localized in partially filled atomic shells. The approximate evaluation of these variational ground states becomes exact in the limit of large coordination number. The result allows the identification of quasi-particle band structures for correlated electron systems. As a first application, we summarize a study of itinerant ferromagnetism in a two-band model, thereby elucidating the co-operation of the Coulomb repulsion and the Hund's-rule exchange. Then, we present results of calculations for ferromagnetic nickel, using a realistic 18 spin-orbital basis of 4s, 4p and 3d valence electrons. Good agreement with the experimental ground-state properties of nickel is obtained. In particular, 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. Finally, we present results for the variational spinwave dispersion for our two-band model.

cond-mat.str-el↗

arXiv1997

Gutzwiller-correlated wave functions for degenerate bands: exact results in infinite dimensions

We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of infinite spatial dimensions. In this limit recent results obtained within the Gutzwiller approximation are seen to become exact for these wave functions. We further show that the Slave Boson mean-field theory for degenerate bands becomes variationally controlled at zero temperature in infinite dimensions. Lastly, we briefly comment on the variational approach to the Anderson transition in strongly correlated electron systems.

cond-mat.str-el↗

arXiv1993

Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional $1/r$-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for half-filled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the~$1/r$-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type wave functions yield reliable predictions on zero temperature phase transitions in low-dimensional, i.e., charge-spin separated systems.

cond-mat↗