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Numerical Computation of Perturbative Continuous Unitary Transformation in Kondo-Necklace Model

Ghasemi, Nader | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45000 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. The fascinating subject of heavy fermion physics in rare-earth and actinide systems has been a challenge for theoretical and experimental investigations for decades. Kondo Necklace model is one of the promising models in the study of strongly-correlated heavy fermion compounds, which is studied in this project.One of the methods to diagonalize a Hamiltonian properly, regardless of system size, is the continuous unitary transformation. In this approach, the Hamiltonian is considered as a function of a flow parameter. The Hamiltonian is transformed to a simpler form (diagonal or band-block diagonal) under a flow equation which is based on applying infinite numbers of infinitesimal unitary transformation [6]. A quantum phase transition (QPT) can happen as a phase transition between different quantum phases at zero temperature. At zero temperature essentially quantum fluctuations lead to a quantum phase transition, where a macroscopic change occurs in physical properties of the system. Kondo-Necklace model was investigated by employing perturbative continues unitary transformations up to fourth order of perturbation [7]. In this thesis, we employed bit-masking method to calculate the ground state energy and energy gap of anisotropies Kondo-Necklace chain and we obtained higher orders of perturbation. Then we investigated the effect of these higher orders on quantum phase transition. We also utilize concurrence to study QPT of KN model in one, two and three dimensions. We implement concurrence, as a measure of bipartite entanglement, to find quantum critical points in the presence of the spontaneous symmetry breaking and observed that imposing the spontaneous symmetry breaking does not modify the ground-state entanglement of the two spins, as defined by the concurrence, in the KN two and three dimensions. We investigated QPT for dimensions more than one and observed for example for two and three dimensions our results are different from previous DMRG results which we concluded that entanglement in this sysytem is not bipartite
  9. Keywords:
  10. Koando-Necklace Model ; Quantum Phase Transition ; Concurrence ; Heavy Fermion Compounds ; Bit-Masking ; Perturbative Continuous Unitary Transformation (PCUT)

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