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Investigation of a Transition from Topologically Ordered Phase to Ferromagnetic Phase

Zarkeshian, Parisa | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45353 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Memarzadeh Esfahani, Laleh
  7. Abstract:
  8. Topologically ordered phases are of great interest in the field of quantum information and quantum computation in order that their degenerate ground states provide a suitable space for coding and processing the quantum information. Such space is resistant to local errors intrinsically. A natural question to ask is to what degree these topological phases are resilient against perturbations and how the transition from topological order to another kind of order occurs.In this thesis, at first we introduce the concept of topological order. We explain the Kitaev model, which is the first introduced topological model on lattice, and study the common properties between topologically ordered systems in the Kitaev model. Also, we introduce the most important measures of topological order. By adding Ising interactions to the Kitaev model and introducing Kitaev-Ising model, we study the competition between topologically ordered phase and the phase with ferromagnetic order. So we consider Kitaev-Ising model on a quasi-one-dimensional lattice, a ladder, and on a two-dimensional periodic lattice, a torus.We need the ground state of the system so as to study the quantum phase transition. Since it is difficult to calculate the ground state of a many-body system, we use some techniques of mapping the ground space and investigate the topological phase transition in Kitaev-Ising model. Finally, we use mean-field analysis to find the transition point and with the help of expectation value of Wilson loop, we confirm topological phase transition in Kitaev-Ising model on a torus
  9. Keywords:
  10. Topological Order ; Topological Phase Transition ; Kitaev-Ising Model

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