Band Hubbard Model Research Articles

A self‐consistent cluster study of the Emery model

AbstractWe calculate Fermi‐surface properties of the Cuprate superconductors within the three band Hubbard model (also called the Emery model) using a cluster expansion for the proper selfenergy. The Fermi‐surface topology is in agreement with angular‐resolved photoemission data for dopings ∼ 20%. We discuss possible violations of the Luttinger sum‐rule for smaller dopings and the role of van‐Hove singularities in the density of states of the Zhang‐Rice singlets. We calculate the shift in the chemical potential upon doping and find quantitative agreement with recent experiments.

Perovskites in high dimensions

We study the (D+1) band Hubbard model on generalizedD-dimensional perovskite structures. We show that in the limit of high dimensions the possible scaling behaviour is uniquely determined via the bandstructure and that the model without direct oxygen-oxygen hopping necessarily scales to the cluster limit. A 1/dimension expansion then leads to at-J like Hamiltonian and the Zhang-Rice analysis becomes rigorous. The large dimension fixed point, in general, still remains the cluster model even when a hopping term between n.n. oxygensites is included. Only for a unique ratio of the oxygen onsite energies to the oxygen-oxygen hopping amplitude is a new fixed point possible, corresponding to a heavy-Fermion Hamiltonian.

Exact diagonalization of a two-dimensional double band Hubbard model on a twelve-site CuO cluster

We present a numerical study of the two-dimensional double band Hubbard model on a twelve-site cluster simulating a copper-oxygen layer. The ground state is antiferromagnetic but magnetic ordering is greatly reduced by doping the cluster with extra holes. The presence of a positive extended-singlet pairing correlation supports a magnetic mechanism for an attractive interaction between holes on second neighbour oxygen sites.

Coupling of electrons and phonons in a doped antiferromagnet

It is well-known that low-energy electronic excitations in high-T c superconductors have energies of the order of the exchange couplingJ, i.e. of the same order as the phonon energies. Therefore, low-energy electronic excitations and phonons should strongly influence each other. To investigate this problem we consider a coupled electron-phonon system. For the electronic degrees of freedom we start from the three band Hubbard or Emery model. In analogy to the transformation of the three band Hubbard model to thet−J model, studied by Zhang and Rice, we derive an effective electron-phonon interaction. Its electronic degrees of freedom are those of thet−J model which couple to the phonons of the original system. The coupling of electrons and phonons is discussed by means of the phonon Green function for a breathing-like mode.

SINGLE PARTICLE AND OPTICAL GAPS IN CHARGE-TRANSFER INSULATORS

We analyze the collective excitations near a Mott-Hubbard and a metal charge transfer insulator transition, using the slave boson technique. We show that the Mott transition can be viewed as an excitonic softening, which takes place when the bound state between the lower and upper Hubbard bands reaches zero energy. The exciton energy is related to the jump of the chemical potential at zero doping. In a charge transfer insulator this mode describes a p-d charge fluctuation, i.e. it is a charge transfer exciton. In the single band Hubbard model the excitonic resonance describes virtual transitions between the lower and the upper Hubbard band. Finally we contrast the behaviour of the collective modes near the Mott transition with and near the Charge Transfer Instability. In the former the exciton energy and the charge compressibility go to zero. In the latter the exciton energy remains finite and the charge susceptibility diverges, causing phase separation.

Phase separation and superconductivity

The thermodynamic stability of two widely investigated models for high Tc superconductivity, the Kondo-lattice and the extended three band Hubbard model, is analyzed in the strong local repulsion regime. Superconducting instabilities in these models are also found. For the first model superconductivity stabilizes the system against phase separation. For the second model the superconducting instabilities occur close to the phase separation region. In both models, therefore, phase separation and superconductivity appear to be related phenomena.

Superconductivity, phase separation and charge transfer instability in the U = ∞ limit of the three band model of the CuO 2 planes

The three band Hubbard model with nearest neighbour repulsion is studied in the U = ∞ limit using the slave boson technique and the large N expansion. A charge transfer (CT) instability is found like in weak coupling theory. The CT instability is always associated with a diverging compressibility leading to a phase separation. The total density and CT susceptibilities are analysed in both the static and dynamic limit to gain insight on the strong mixing between the density fluctuations and the excitonic modes. The evaluation to order 1 N of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.

Quantum Monte Carlo Simulations of a CuO2 Model

The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. Here we discuss the properties of the two-dimensional CuO2 layers common to these materials in terms of a three- band Hubbard model. We describe how recently devel oped quantum Monte Carlo simulation techniques al low one to calculate the physical properties of strongly interacting many-electron systems and discuss the re sources required for such simulations. Then we review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and supercon ducting correlations in the three-band Hubbard model. We conclude with a discussion of future goals.

Spin analog method for collective modes of the Hubbard model

We make use of a canonical transformation relating the positive U and negative U sectors of the one band Hubbard model to study the global SU(2) pseudospin symmetry in the model, and to investigate the structure of the collective excitation spectrum from a superconducting ground state in the model. New collective modes in this model associated with the SU(2) pseudospin symmetry, recently discussed by Zhang, appear in the pseudo-spinwave spectrum of the transformed problem. Consequences of this mapping for a self dual generalization of the Hubbard model are also discussed.

Monte Carlo simulations in fermionic systems: The three band Hubbard model case

We present an application of the so-called determinantal method for the Monte Carlo simulation of fermionic systems, for the case of the two-dimensional three band Hubbard model. Our analysis of the conjugate gradient procedure shows that a proper treatment of the linear system of equations is necessary in order to avoid introducing asymmetries which are responsible for numerical instabilities in the algorithm.

SO(4) Symmetry of the Hubbard Model and its Experimental Consequences

The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.

PHASE SEPARATION AND SUPERCONDUCTIVITY IN THE U=∞ LIMIT OF THE EXTENDED MULTIBAND HUBBARD MODEL

The three band Hubbard model with nearest neighbour repulsion is studied in the U=∞ limit using the large N expansion technique to order [Formula: see text]. A charge transfer (CT) instability is found like in weak coupling theory. However at small doping a major role is played by the Brinkman-Rice point. The CT instability is always associated with a diverging compressibility leading to a phase separation. The evaluation to order [Formula: see text] of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.

Local anharmonic vibrations strong correlations and superconductivity: A quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-T c materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.

Numerical study of slave boson mean field equations for the Hubbard model

We consider the one band Hubbard model in the Slave Boson formulation first introduced by Kotliar and Ruckenstein. Applying a modified Mean Field Approximation (MFA), which allows for broken symmetry states, we numerically determine the values of the involved Bose fields at the saddle point. Our data for local Fermion correlation functions agree surprisingly well with data obtained in recent Quantum Monte Carlo calculations.

Quantum Monte Carlo simulations for high- Tc models

Numerical simulations were carried out using a projector quantum Monte Carlo method pioneered by Sorella et al. Ground state energies are presented for the single band Hubbard model for system sizes 4 x 4 to 8 x 8. The Hubbard model coupled to a two-level system (e.g. bridging oxygen) was also studied. Enhancement of superconducting susceptibilities indicates the possibility of high- T c superconductivity.

S-wave superconductivity in the presence of a strong coulomb repulsion

We study the occurence of s-wave superconductivity in a single band Hubbard model, in the large U limit and with a nearest neighbour attraction V s. This attraction V s must exceed a critical value V c s to make superconductivity stable. However V c s is suppressed if second neighbour hopping is included in the Hubbard model.

Spin fluctuations, spin bags and the high T c superconductivity

Abstract The magnetic properties of the half-filled one band Hubbard model is studied within the random phase approximation (RPA) above the mean field spin-density-wave (SDW) background. The spin wave spectrum and the sublattice magnetization are shown to interpolate smoothly between the weak and strong coupling limits. A hole in the SDW background is self-trapped in a region of reduced SDW amplitude and forms an object which we call the spin bag. The attraction among the two holes results due to the tendency to share the region of reduced SDW amplitude. A detailed calculation based on the RPA above the SDW background support this picture. The symmetries and the nodes of the resulting pairing gap are discussed.

Magnetic and pairing correlations in a three band Hubbard model

Abstract The two dimensional CuO 2 sheets common to both the superconducting oxides La 1−x Sr x CuO 4 and YBa 2 Cu 3 O 7−δ are believed to play an important role in the high transition temperatures of these materials. In this contribution, we make use of some recently developed techniques for the simulation of systems of strongly interacting electrons at low temperatures to study a multi-band positive-U Hubbard model. As in the single band model, doping away from one hole per unit cell rapidly decreases antiferromagnetic correlations. In contrast to the single band model, enhancement of the extended s-wave pairing susceptibility is a feature of a number of regimes of interaction strengths.

On d-wave pairing in one band Hubbard model

The strong correlated one band or t-J model is considered. An excitation spectrum allowing for the superconducting pairing is obtained by employing the projection technique for the Green function in terms of Hubbard operators. By taking into account the local constraint which eliminates double site occupancy an equation for d-wave gap is obtained.

Comment on the one band Hubbard model for the superconducting Cu oxides

We present a simple cluster calculation which strongly suggests that the one band Hubbard model is not sufficient for a complete description of the CuO2 layers in high Tc superconductors.