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Investigation of Strongly Correlated Electron Systems with Dynamical Mean Field Theory

Nourafkan, Reza | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39434 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Nafari, Naser
  7. Abstract:
  8. In this thesis we study the strongly correlated electron systems and investigate the interply between electron-electron and electron-phonon interactions using a non-perturbative method, known as Dy- namical Mean Field Theory (DMFT). This method is capable of going beyond standard perturbation techniques. DMFT is by construction a local theory which neglects spatial correlations. In a first step, we approach the problem of interplay between these two interactions in the normal state of cuprate materials using the Holstein-Hubbard model. We then introduce orbital degrees of freedom, and study the polaron crossover and the pairing transition for a two-orbital model with Jahn-Teller coupling to a two-fold degenerate phonon mode. The evolution from weak to strong coupling in this case is reminiscent of the behavior of the single-band Holstein model: The polaron crossover in which the electrons and phonons become strongly entangled occurs for a weaker coupling than the bipolarons binding, which gives rise to a metal-nsulator transition. Interestingly, a single bipolaronic transition takes place also when the two bands have significantly different bandwidths, as opposed to the case of repulsive Hubbard-like interactions for which an orbital-selective Mott transition has been reported. This behavior is related to the inter-orbital nature of the Jahn-Teller coupling.
    We also study the anti-ferromagnetic phase (AF) of the half-filled multi-channel Kondo lattice model. Our calculations for the two channel case show the existence of an AF phase for all coupling strengths of physical interest, while for the single channel case there is a quantum phase transition to the singlet Kondo insulator phase which destroys the AF phase. In fact, in addition to the RKKY interaction and the Kondo screening effect, there is a novel type of superexchange present in the two- channel Kondo lattice model that leads to AF phase at half-filling. We finally study the phase diagram of the Holstein-Kondo lattice model, including both the Kondo exchange coupling and the electron- phonon coupling constants, characterized by J and g. We find that the model presents the physics of the Kondo insulator when the exchange oupling, J , is dominant and atransition to correlated metal takes place for small J and intermediate e-ph coupling, g. Moreover, a bipolaronic-metal insulator transition takes place for small J and large g
  9. Keywords:
  10. Dynamical Mean-field Theory ; Electron-Phonon Interaction ; Strongly Correlated Electron Systems ; Polaron and Bipolaron ; Kondo Lattice Model

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