Long-range orders in the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation corrected by Lacroix-Lyon-Caen and Cyrot. The static susceptibility method is used. In the strong scattering limit, a ferromagnetic instability for 1 < N < 2 and 2 < N < 3 is confirmed. It is proved that there is no antiferromagnetic or charge-order instability for any N.     

Alloy analogy of the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation. In the strong coupling limit, a ferromagnetic instability occurs when 1 < N < 2 and 2 < N < 3. We compare this approximation with other approximations and with the exact results.     

Ferromagnetism in the degenerate Hubbard model

We study the ground state of the doubly degenerate Hubbard model in the strong coupling limit. For this limit, we obtain new exact results: when there are N ? 1 electrons, the ground state is ferromagnetic and there is a ferromagnetic orbital ordering; when the number of electrons is between N and 2N, the ground state is also ferromagnetic due to the intra-atomic Hund's coupling. For this second case, we give an estimate of the Curie temperature.     

Orbital-selective mott transitions in the degenerate Hubbard model

We investigate the Mott transitions in two-band Hubbard models with different bandwidths. Applying dynamical mean field theory, we discuss the stability of itinerant quasiparticle states in each band. We demonstrate that separate Mott transitions occur at different Coulomb interaction strengths in general, which merge to a single transition only under special conditions. This kind of behavior may be relevant for the physics of the single-layer ruthenates, Ca2-xSrxRuO4.     

The effect of zero-point spin wave motions on the hole propagation in the strongly correlated Hubbard model

The kinetic energy of holes doped in a two dimensional antiferromagnetic state is dicussed, taking into account the effect of zero-point spin wave motions. The lower band edge of the hole density of states is estimated from its lower order moments in the strong electron correlation limit. A relatively large narrowing of the density of states is obtained, nearly the same as that of the RVB case. Consequences of the result are discussed in connection with the relative stability between the antiferromagnetic state and the RVB state.     

The extended Hubbard model in the ionic limit

In this paper, we study the Hubbard model with intersite Coulomb interaction in the ionic limit (i.e. no kinetic energy). It is shown that this model is isomorphic to the spin-1 Ising model in presence of a crystal field and an external magnetic field. We show that for such models it is possible to find, for any dimension, a finite complete set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the relevant Green's functions and correlation functions can be obtained. These expressions are formal because these functions depend on a finite set of unknown parameters, and only a set of exact relations among the correlation functions can be derived. In the one-dimensional case we show that by means of algebraic constraints it is possible to obtain extra equations which close the set and allow us to obtain a complete exact solution of the model. The behavior of the relevant physical properties for the 1D system is reported.     

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)     

Superconductivity in a correlated two-dimensional Hubbard model: A theoretical study

In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use Green's function method to obtain the order parameter Δ and the superconducting critical temperature T_c. The results show that for fixed values of the superconducting attractive potential U (U<0), the gap increases for low temperatures, whereas diminishes abruptly as the temperature increases. The effect of pressure can be discussed, varying the next-nearest-neighbors hopping t₂, yielding a change in T_c, and also in Δ₀.     

Coupling of fluctuation modes in the disordered strongly attractive Hubbard model

The coupling of two different types of soft modes related to interaction-generated superconducting and disorder-generated (pseudo)diffusive fluctuations in the large negative-U Hubbard model with random local energies is studied in the framework of a Grassmann field theoretic approach with modified semionic Matsubara frequencies. In leading loop order it is found that the sound-like order parameter phase fluctuation mode retains its massless nature with only its velocity being modified, as expected from the generalized Ward identity. The disorder-induced fluctuations which are originally completely local due to the locality of disorder correlations acquire true diffusive behaviour by interaction effects in the superconducting phase.     

Superconducting instability in the large-U limit of the two-dimensional Hubbard model

We have investigated numerically the pairing instabilities of Gutzwiller wavefunctions. These are equivalent to a certain form of the resonant valence bond wavefunction. The case considered is a nearly half-filled two dimensional band with interactions given by a Hubbard model with large on-site Coulomb interactions. We find that the paramagnetic normal state is unstable tod-wave pairing but stable againsts-wave pairing. The antiferromagnetic state is marginally stable against both types of pairing. These results can be explained as an interference effect resulting in enhanced antiferromagnetic spin correlation in the paired state.     

Polaron effects in the nearly atomic limit of the Hubbard model

The Hubbard Model of electron correlation effects in solids is unified with Holstein's molecular crystal model for small polarons as a first step in studying electron-phonon coupling in π-bonded organic solids. Some implications of the electron-lattice coupling on both the single particle excitation spectrum and the effective Heisenberg exchange energy are discussed.     

Charge orderings in the atomic limit of the extended Hubbard model

The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for charge orderings are obtained. The phase diagrams include three types of charge ordered phases and the nonordered phase. The system exhibits very rich structure and shows unusual multicritical behavior. In the limiting case of t_ij=0, the EHM is equivalent to the pseudospin model with single-ion anisotropy , exchange interaction W in an effective magnetic field . This classical spin model is analyzed using the MC method for the canonical ensemble. The phase diagram is compared with the known results for the Blume-Capel model.