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

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

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

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

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

Effects of Disorder on Superconductivity of Systems with Coexisting Itinerant Electrons and Local Pairs

We study the influence of diagonal disorder (random site energy) of local pair (LP) site energies on the superconducting properties of a system of coexisting local pairs and itinerant electrons described by the (hard-core) boson-fermion model. Our analysis shows that the properties of such a model with s-wave pairing can be very strongly affected by the diagonal disorder in LP subsystem (the randomness of the LP site energies). This is in contrast with the conventional s-wave BCS superconductors, which according to the Anderson's theorem are rather insensitive to the diagonal disorder (i.e. to nonmagnetic impurities). It has been found that the disorder effects depend in a crucial way on the total particle concentration n and the LP level position DELTA_o and depending on the parameters the system can exhibit various types of superconducting behaviour, including the LP-like, intermediate (MIXED)and the 'BCS'-like. In the extended range of {n,DELTA_o} the superconducting ordering is suppressed by the randomness of the LP site energies and the increasing disorder induces a changeover from the MIXEDlike behaviour to the BCS-like one, connected with abrupt reduction of T_c and energy gap to zero. However, there also exist a definite range of {n,DELTA_o} in which the increasing disorder has a quite different effect: namely it can substantially enhance T_c or even lead to the phenomenon which can be called disorder induced superconductivity. Another interesting effect is a possibility of a disorder induced bound pair formation of itinerant electrons, connected with the change-over to the LP-like regime.Comment: 18 pages, 12 figure

Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model

A strong-coupling expansion is applied to the anharmonic Holstein model and to the Holstein-Hubbard model through fourth order in the hopping matrix element. Mean-field theory is then employed to determine transition temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic effects are not easily mimicked by an on-site Coulomb repulsion, and that anharmonicity strongly favors superconductivity relative to charge-density-wave order. Surprisingly, the phase diagram is strongly modified by relatively small values of the anharmonicity.Comment: 34 pages, typeset in ReVTeX, 11 encapsulated postscript files include

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

Local Moment Formation in the Periodic Anderson Model with Superconducting Correlations

We study local moment formation in the presence of superconducting correlations among the f-electrons in the periodic Anderson model. Local moments form if the Coulomb interaction U>U_cr. We find that U_cr is considerably stronger in the presence of superconducting correlations than in the non-superconducting system. Our study is done for various values of the f-level energy and electronic density. The smallest critical U_cr values occur for the case where the number of f- electrons per site is equal to one. In the presence of d-wave superconducting correlations we find that local moment formation presents a quantum phase transition as function of pressure. This quantum phase transition separates a region where local moments and d-wave superconductivity coexist from another region characterized by a superconducting ground state with no local moments. We discuss the possible relevance of these results to experimental studies of the competition between magnetic order and superconductivity in CeCu_2Si_2.Comment: 4 pages. accepted for publication in Phys. Rev.