The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model

We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points.Comment: 12 pages, 7 figures; final version, pdf-ReVTeX; corrected typos in reference; submitted to Journal of Physics: Condensed Matte

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.Comment: 15 pages, 9 figures; pdf-ReVTeX, final version, corrected typos; submitted to Journal of Physics: Condensed Matte

Anisotropic Superconductivity in the Induced Pairing Model

The model of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems is studied for anisotropic pairing symmetry. The phase diagram is presented and the phase fluctuations effects are analyzed within the Kosterlitz-Thouless scenario.Comment: 4 pages, 2 figures. Physica B (in press), Proceedings of the International Conference on Strongly Correlated Electron Systems, Ann Arbor, Michigan, August 6-10, 200

Band and filling controlled transitions in exactly solved electronic models

We describe a general method to study the ground state phase diagram of electronic models on chains whose extended Hubbard hamiltonian is formed by a generalized permutator plus a band-controlling term. The method, based on the appropriate interpretation of Sutherland's species, yields under described conditions a reduction of the effective Hilbert space. In particular, we derive the phase diagrams of two new models; the first one exhibits a band-controlled insulator-superconductor transition at half-filling for the unusually high value $U_c=6 t$; the second one is characterized by a filling-controlled metal-insulator transition between two finite regions of the diagram.Comment: 5 pages, REVTEX, 2 eps figure

Real space inhomogeneities in high temperature superconductors: the perspective of two-component model

The two-component model of high temperature superconductors in its real space version has been solved using Bogoliubov-de Gennes equations. The disorder in the electron and boson subsystem has been taken into account. It strongly modifies the superconducting properties and leads to local variations of the gap parameter and density of states. The assumption that the impurities mainly modify boson energies offers natural explanation of the puzzling positive correlation between the positions of impurities and the values of the order parameter found in the scanning tunnelling microscopy experiments.Comment: 19 pages, IOPP style include

Effect of disorder on superconductivity in the boson-fermion model

We study how a randomness of either boson or fermion site energies affects the superconducting phase of the boson fermion model. We find that, contrary to what is expected for s-wave superconductors, the non-magnetic disorder is detrimental to the s-wave superconductivity. However, depending in which subsystem the disorder is located, we can observe different channels being affected. Weak disorder of the fermion subsystem is responsible mainly for renormalization of the single particle density of states while disorder in the boson subsystem directly leads to fluctuation of the strength of the effective pairing between fermions.Comment: 7 pages, 6 figures. Physical Review B (accepted for publication

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matte

Signatures of polaronic excitations in quasi-one-dimensional LaTiO3.41_{3.41}

The optical properties of quasi-one-dimensional metallic LaTiO$_{3.41}$ are studied for the polarization along the $a$ and $b$ axes. With decreasing temperature modes appear along both directions suggestive for a phase transition. The broadness of these modes along the conducting axis might be due to the coupling of the phonons to low-energy electronic excitations across an energy gap. We observe a pronounced midinfrared band with a temperature dependence consistent with (interacting) polaron models. The polaronic picture is corroborated by the presence of strong electron-phonon coupling and the temperature dependence of the dc conductivity.Comment: 5 pages, 5 figure

Temperature and filling dependence of the superconducting π\pi-phase in the Penson-Kolb-Hubbard model

We investigate in the Hartree Fock approximation the temperature and filling dependence of the superconducting $\pi$-phase for the Penson-Kolb-Hubbard model. Due to the presence of the pair-hopping term, the phase survives for repulsive values of the on-site Coulomb interaction, exhibiting an interesting filling and temperature dependence. The structure of the self-consistent equations peculiar to the $\pi$-phase of the model allows to explicitly solve them for the chemical potential. The phase diagrams are shown and discussed in dimension 2 and 3. We also show that, when a next-nearest neighbours hopping term is included, the critical temperature of the superconducting region increases, and the corresponding range of filling values is shifted away from half-filling. Comparison with known exact results is also discussed.Comment: 20 pages, REVTEX, 8 eps figure