The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model with attractive on-site interaction of the electrons are solved numerically at low temperatures. At low temperatures the dominant states consist of spin-paired electrons (Cooper-pair--like) and excitations of such pairs (without breaking up the singlet bound states). A critical field (energy required to depair a Cooper pair) is obtained at T=0 (note that the superconducting
Tc=0), which disappears for T\ensuremath{\ne}0. The specific heat is linear in temperature, and the dependence of the coefficient \ensuremath{\gamma} on band filling and magnetic field is discussed. The excitation spectrum shows some analogies with that of resonant valence bonds in two dimensions.
Two aspects of strongly correlated electron systems are studied in this thesis. Hubbard-type models are thought to be at the basis of high-critical-temperature superconductivity. One interaction which has not had much study is the nearest-neighbour hopping of on-site singlet pairs. We refine earlier renormalization group arguments and, using the density-matrix renormalization group method, numerically confirm their prediction that a spin gap opens at infinitesimal pair-hopping amplitude V > 0 in the one-dimensional tight-binding model. We also find a phase separation transition at a finite V > 0 as well as a spin-gap transition at a finite V < 0. The exotic magnetic behaviour of heavy-fermion materials involves an interplay between the screening of local moments from each other and the formation of a magnetic state of long range order. While the single-impurity Kondo Hamiltonian is thought to model some aspects of this behaviour, the properties of the Kondo lattice model away from half-filling are largely unknown. We determine the presence of a spin-gap region in the phase diagram of the one-dimensional Heisenberg-Kondo lattice model and make predictions about certain concealed dimerization order parameters.
The exact solution via Bethe's ansatz to a model consisting of two parabolic bands of electrons with local attractive and repulsive interactions is presented. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the crystal-field splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states and a threshold magnetic field is required to overcome the binding energy. The low-T specific heat is proportional to T, except at critical points where C\ensuremath{\propto}
T1/2.
The two-band model describing strongly hybridized degenerated electron states in a chain is proposed and solved exactly by means of the Bethe ansatz. The fermions of the subbands interact with each other via one-particle and one-particle correlated on-site hybridized interactions. The chain of electrons is reduced to the model with two noninteracting subbands with a given total number of electrons, in which fermions interact via different effective constants of interactions. In the case of strong hybridized interaction the on-site repulsive interaction is compensated by hybridized interaction, which leads to an effective attractive interaction between particles and the formation of spinless bound states of Cooper type. This electron liquid component determines both heavy fermion- and superconducting-type behavior of electron properties.
We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J (1) (parallel spins), J (2) (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V ).As a first step we find the eigenvalues Eα and eigenvectors |E α of the dimer and we represent each partial Hamiltonian Eα|Eα Eα| (α = 1, 2, . . ., 16) in the second quantization with the use of the Hubbard and spin operators.Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons.A typical feature is the appearance of two generalized t-J interactions ascribed to two different energy levels which do not vanish even for U = J (1) = J (2) = V = 0 and their coupling constants are equal to ±t in this case.In the large U -limit for J (1) = J (2) = V = 0 there is only one t-J interaction with coupling constant equal to 4t 2 /|U | as in the case of a real lattice.The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U = J (1) = J (2) = V = 0 and t = 0.The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels.It qualitatively explains the origin of the phase diagram of the model.We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.