Contributions to the theory of ferromagnetism in the degenerate Hubbard model

The possibility of ferromagnetic ordering in a generalized Hubbard model with allowance for degeneracy and for infinite Hubbard energy is studied. The region of existence of ferromagnetism for electron density greater than 1 is determined. It is shown that for electron density less than 1 ferromagnetism exists only in special cases when the Fermi surface passes near van Hove singularities. Zh. éksp. Teor. Fiz. 112, 2223–2236 (December 1997)     

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Using a universal relation between electron filling factor and ground state energy,this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime,and demonstrates that in contrast to the usual Hubbard model(gc = 1/2),the dimensionless coupling strength parameter g c heavily depends on the electron filling,and it has a "particle-hole" symmetry about electron quarter filling point.As increasing the nearest neighbouring repulsive interaction,the single particle spectral weight is transferred from low energy to high energy regimes.Moreover,at electron quarter filling,there is a metal-Mott insulator transition at the strong coupling point gc = 1/4,and this transition is a continuous phase transition.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

Density of states and dispersion of quasiparticles in the Emery model: Nonlocal path-integral Monte Carlo algorithm

The spectral density of states for a 108-site Cu₃₆O₇₂ cluster in the two-dimensional three-band Emery model is reconstructed with the aid of a path integral Monte Carlo algorithm. Dispersion relations are obtained for quasiparticles in the upper Hubbard band and in the correlated-states band; this corresponds to electron and hole doping of high-T _c superconductors. The form of the isoenergy surfaces is close to the experimentally observed form and confirms the existence of singularities in the density of states near the Fermi level. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 860–865 (10 June 1996)     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Real‐space multiple‐scattering Hubbard model calculations for d‐ and f‐state materials

Calculations are presented of the electronic structure and X‐ray spectra of materials with correlated d‐ and f‐electron states based on the Hubbard model, a real‐space multiple‐scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random‐phase approximation. The combination of the real‐space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core‐level X‐ray spectra. Results are presented for the projected density of states and X‐ray absorption spectra for transition metal‐ and lanthanide‐oxides. Results are found to be in good agreement with experiment.     

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.     

Effect of hole doping on the electronic structure and the Fermi surface in the Hubbard model within norm-conserving cluster pertubation theory

The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U. The concentration dependence of the Fermi surface strongly depends on hopping to second (t′) and third (t″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.     

Quasi‐particle peak due to magnetic order in strongly correlated electron systems

We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP¹ representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.     

Rest Energy of Classical Self Fields of Point Gravitating Sources

A variant of Brans-Dicke theory is discussed in which the singularities of electric, scalar and metric sector of classical self fields of a point gravitating source are in Jordan frame suppressed and their energy - momentum tensor is integrable. The total energy of the classical electron Coulomb field is finite and in accordance with special relativistic expression m ₀ c ². The same may be said with respect to total rest energy of the quasi-Coulomb field, i.e. the scalar self-field of the source in the case of electron and in the case of a source with zero electric charge. Although (pseudo-)Einstein equations in (pseudo-)Pauli frame are modified, all experimental predictions concerning gravitational effects of macroscopic (celestial) bodies are in accordance with that of GRT.     

A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong coupling negativeU Hubbard model

We calculate fluctuation effects on Bose condensation type superconductivity in the strong coupling negative U Hubbard model by means of a new loop expansion. Our method is based on a spin-dependent modification of the Popov-Fedotov trick. We replace the Popov-Fedotov chemical potential by a fictitious imaginary magnetic field. This field is absorbed in spindependent semionic Matsubara frequencies, which allows for a mixed statistics representation of the anisotropic quantum spin 1/2 Heisenberg model. We report results at one loop order for the superconducting order parameter , for the critical temperature, for the chemical potential, and for the excitation spectra both above and belowT _c. We identify mean field results in zeroth loop order and we find both dimensional and filling (v-)depending singularities in interaction fluctuations at one loop order. Renormalization of dimensional singularities is carried out in 4 dimensions. Divergencies withv (1–v)0 in the dilute limits indicate the breakdown of mean field solutions, but superconductivity persists for arbitrarily smallv(1–v) if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma model.     

Correlation mediated superconductivity in a “HighT c ” model

We present a simple model to account for the High-T _c perovskite superconductors. The superconducting mechanism is purely electronic and comes from local Hubbard correlations. The model comprises a Hubbard model for the Copper sites with a single particle Oxygen band between the two Copper Hubbard bands. The electrons move only between nearest neighbour atoms which are of different types. Using two very different approximation schemes, one related to Slave-Boson mean field theory and the other based on an exact local Fermion transformation, we show the possibility of Copper-Oxygen or a mixture of Copper-Oxygen and Oxygen-Oxygen pairing. We believe that the most promising situation for superconductivity is with the Oxygen band over half-filled and closer in energy to the lower Hubbard band.     

Single-hole state in half-filled 2D Hubbard model

Summary We have investigated the ground state of a single hole in the half-filled Hubbard model on a 2D square lattice using the coupled-cluster method. In particular we obtained an analytical expression of the hole energy dispersion function ɛ(k) which is consistent with earlier studies on thet-J model in the strong-coupling limit. An appreciable discrepancy on the hole energy bandwidth is, however, observed between the Hubbard model and thet-J model. We believe that this discrepancy is due to the absence of the three-site interaction term in thet-J model.     

Antiferromagnetism in the Hubbard model

The energy spectrum of the two-sublattice Hubbard model is obtained in the static-fluctuation approximation. It is shown how the structure of the energy spectrum is modified as the parameters of the Hubbard model are varied. The ground state of the simple Hubbard model of dimension d=2 is the dielectric antiferromagnetic state. The author derives a consistency equation for the magnetization, which has an antiferromagnetic solution. Fiz. Tverd. Tela (St. Petersburg) 39, 1594–1599 (September 1997)     

Theory of superconductivity in strongly correlated materials: Application to cuprate superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high T _c proportional to the Fermi energy. T _c dependence on lattice constants (or pressure) and an oxygen isotope shift of T _c are explained. The text was submitted by the author in English.     

The Weak Energy Condition and Singularities in Classical Free N = 1 Supergravity

With the use of the modification of the weak energy condition for theories with torsion developed by Hehl, we analyse classical free N = 1 supergravity in the hope that spin-spin contact interactions may avert singularities, as happens in the neutrinic case. We find that this does not happen, since the appearence of singularities is conditioned by the cosmological model of the gravitino field in consideration. We present a very simple singularity free model for a spatially homogeneous Rarita-Schwinger field in a Robertson-Walker spacetime.     

On the effect of van Hove singularities on the critical field of type-II superconductors

The properties of the two-dimensional Hubbard model with strong repulsion are studied under the condition that the Fermi surface passes through van Hove singularities. The upper critical field is calculated under conditions where there is no relaxation. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 71–76 (10 January 1997)     

Excitation spectrum of one-dimensional extended ionic Hubbard model

We use perturbative continuous unitary transformations (PCUT) to study the one dimensional extended ionic Hubbard model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, V. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system; (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V = 0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of V there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion U is to split singlet and triplet collective excitation branches, while V tends to pull the singlet branches below the continuum to make them bound states.