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Continuous Unitary Transformation and Quantum Phase Transition in Kondo-necklace Model

Rahimi Movassagh, Mahsa | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41551 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. Strongly correlated electron systems are an interesting topic among condensed matter systems. The electrons in such systems are strongly correlated to each other in a way that the behavior of the systems cannot be described by single particle theories. One of the most famous of these systems are heavy fermionic materials which are called so due to heavy quasi particles mass.
    This kind of materials have been investigated via different methods. The most im-portant model that can describe characteristics of these materials is Kondo lattice model. When we are only interested in magnetic properties of them, the model can be reduced to Kondo-necklace model which only involves with spin degrees of freedom. Iinteractions between the spin of itinerant electrons and between the spin of localized electrons and itinerant ones define this model. This model can predict phase transitions between a Fermi liquid and antiferromagnetically ordered phase. The effect of anisotropy of interaction between different spins including z component have been investigated with different methods [32, 33, 34].
    In the present work we have firstly studied a method of diagonalizing Hamiltonian which is called continuous unitary transformation. we have also studied perturba-tive continuous unitary transformation. Then we have investigated the dependence of the quantum cirtical points on the anistropy parameters of two and three dimen-sion via this method. Analytic expression for ground state energy up to 4th order has been calculated via perturbation continuous unitary transformation. We have also obtained excitation energy up to 3th order which is vanished at critical points. This behavior can shows gap dependence on the anisotropy parameters. Our re-sults are in good agreement with those from previous approaches such as me field theory and Green function approach [32, 34]. We have also obtained differ-ent orders of pade approximation of gap energy in two and three dimension which show good agreement with our results
  9. Keywords:
  10. Koando-Necklace Model ; Quantum Phase Transition ; Continuous Unitary Transformation ; Band Gap

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