Green’s Function Method in the Theory of Strongly Correlated Pseudospin-Electron Systems

  • I. V. Stasyuk
  • A. M. Shvaika


An important role of the apex oxygen anharmonic vibrations in the phase transition into superconducting state has been already mentioned.1,2 Within the models describing the coupling of correlated electrons to vibrational degrees of freedom one can consider the model for which the Hubbard Hamiltonian is supplemented with the interaction of electrons with local anharmonic vibrations where the latter are represented by pseudospin variables. The Hamiltonian of the pseudospin-electron model derived in this way has the following form3
$$H = \mathop{\sum }\limits_{i} {{H}_{i}} + \mathop{\sum }\limits_{{ij\sigma }} {{t}_{{ij}}}a_{{i\sigma }}^{\dag }{{a}_{{j\sigma }}},$$
$${{H}_{i}} = U{{n}_{{i \uparrow }}}{{n}_{{i \downarrow }}} + {{E}_{0}}({{n}_{{i \uparrow }}} + {{n}_{{i \downarrow }}}) + g({{n}_{{i \uparrow }}} + {{n}_{{i \downarrow }}})S_{i}^{z} - \Omega S_{i}^{x} - hS_{i}^{z}.$$
The similar Hamiltonian was also proposed in Ref. 4 for the description of the propagation of the holes through a lattice of anions with filled shells. The investigations of possible superconducting pair correlations were performed in the framework of model (1) using numerical Monte-Carlo simulations5 and Green’s functions method.6 In previous papers7,8 we considered single-electron spectrum, electron-electron exchange interaction and static dielectric susceptibility of the model (1).


Dielectric Susceptibility Tunneling Splitting Anharmonic Vibration Charge Density Fluctuation Generalize Random Phase Approximation 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • I. V. Stasyuk
    • 1
  • A. M. Shvaika
    • 1
  1. 1.Institute for Condensed Matter PhysicsNational Academy of Sciences of UkraineLvivUkraine

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