Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency . Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case , the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime overcomes the energy of the purely electronic system . In the antiadiabatic case, , polaron formation is instead driven by the condition of a large ionic displacement (g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed. Received 15 February 1999     

Off-diagonal long-range order, η-pairing,and Friedel oscillations in high Tc cuprate superconductors and the ground state of the extended Hubbard model

It is argued that Yang's η-paired wave function is the electronic ground state of high T_c cuprate superconductors. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 675–684, 1997     

Magnetic properties of small Fe clusters: a nonorthogonal H amiltonian study

We calculate the magnetic properties of small FeN clusters(N=2～7,9,13,15) by using a parameterized Hubbard tight-binding sp d-band model Hamiltonian, with the parameters obtained from nonorthogonal Ham il tonian parameters. the average magnetic moments, and the spin-polarized charge distribution within clusters are in agreement with those obtained by first-prin ciple and tight-binding calculations. The effect of the nonorthogonal basis is discussed.     

“Linearized” dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The “linearized DMFT” yields plausible results for the complete geometry dependence of the critical interaction. Received 6 May 1999 and Received in final form 2 July 1999     

First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999     

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

Dynamical mean-field study of the Mott transition in thin films

The correlation-driven transition from a paramagnetic metal to a paramagnetic Mott-Hubbard insulator is studied within the half-filled Hubbard model for a thin-film geometry. We consider simple-cubic films with different low-index surfaces and film thickness d ranging from d=1 (two-dimensional) up to d=8. Using the dynamical mean-field theory, the lattice (film) problem is self-consistently mapped onto a set of d single-impurity Anderson models which are indirectly coupled via the respective baths of conduction electrons. The impurity models are solved at zero temperature using the exact-diagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the finite film thickness are found to be the more pronounced the lower is the film-surface coordination number. For the comparatively open sc(111) geometry we find a strong layer dependence of the quasi-particle weight while it is much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction strength U _c2 (d) at which all effective masses diverge and there is a unique strength U _c1 (d) where the insulating solution disappears. U _c2 (d) and U _c1 (d) gradually increase with increasing thickness eventually approaching their bulk values. A simple analytical argument explains the complete geometry and thickness dependence of U_c2. U_c1 is found to scale linearly with U_c2. Received 19 August 1998     

Thermal evolution of hole dynamics in the large-dimensional model

The dynamics of a single hole in the t - J model is solved exactly for all temperature, T, in the limit of large spatial dimensions, , using the Feenberg renormalized perturbation series. We focus in particular on single-particle spectra, together with optical and static hole conductivities. Explicit results are illustrated for a Bethe lattice, and exemplify the continuous thermal evolution of the underlying string picture from the T =0 string-pinned limit through to the paramagnetic phase. Quenched site-disorder is also readily incorporated, exact results thereby being obtained for the interplay between disorder and thermally-induced hole dynamics. Received 16 September 1998     

Evidence for d-wave superconductivity in the repulsive Hubbard model

We perform numerical simulations of the Hubbard model using the projector Quantum Monte Carlo method. A novel approach for finite size scaling is discussed. We obtain evidence in favor of d-wave superconductivity in the repulsive Hubbard model. For U=4, is roughly estimated as K. Received 8 September 1998