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

Some exact results for the zero-bandwidth extended Hubbard model with intersite charge and magnetic interactions

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site $U$ interaction and intersite (ii) density-density interaction $W$ and (iii) Ising-like magnetic exchange interaction $J$ (between the nearest-neighbors). We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D-chain in two particular cases: (a) $W=0$ and $n=1$; (b) $U\rightarrow+\infty$ and $n=1/2$ ($W\neq 0$, $J\neq 0$). We obtain the exact formulas for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat ($c$), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of $c$ involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state.Comment: 4 pages, 2 figures; pdf-ReVTeX; updated references; presented at The European Conference PHYSICS OF MAGNETISM 2014 (PM'14), June 23-27, 2014, Poznan, Poland; submitted to Acta Physica Polonica

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

Effects of diagonal disorder on Charge Density Wave and Superconductivity in local pair systems

We analyse the influence of diagonal disorder (random site energy) on Charge Density Wave (CDW) and Superconductivity (SS) in local pair systems which are described by the model of hard core charged bosons on a lattice. This problem was previously studied within the mean field approximation for the case of half filled band (n = 1). Here we extend that investigation to the case of arbitrary particle concentration (0 < n < 2) and examine the phase diagrams of the model and the behaviour of superfluid density as a function of n and the increasing disorder. Depending on the strength of random on-site energies, the intersite density-density repulsion and the concentration the model can exhibit several various phases, including homogeneous phases: CDW, SS and Bose-glass (NO) as well as the phase separated states: CDW-SS, CDW-NO and particle droplets. The obtained results for SS phase are in qualitative agreement with the available Monte Carlo calculations for two dimensional lattice. Also, in a definite range of parameters the system exhibits the phenomena which we call a disorder induced superconductivity and a disorder induced charge ordering.Comment: 21 pages, 8 figure