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Robustness of Topological Order under Temperature Fluctuations

Bahrami, Faranak | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48194 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Memarzadeh Esfahani, Laleh
  7. Abstract:
  8. Systems which have local ordered parameters are fragile and sensitive to local errors.Among these systems, quantum systems with local order face errors due to interaction with the environment, which eventuates in destruction of information. It goes without saying that quantum error-correction is a very difficult task to do. This happens in the grounds that not only is the observation of qubits impossible, but also based on no-cloning theory in quantum mechanics, there is no way to have copies of these qubits. Therefore, the interaction of quantum systems with the environment should be controlled in the way that in which we can correct errors using error-correction condition.However, there is another type of quantum orders that have non-local order, eventuating in robustness of these systems under local errors. Thus, these systems, which have topological order, have gained a considerable amount of interest. In T=0, local errors do not cause any errors in topological ordered systems due to the intrinsic features of degenerate ground state, but by increasing temperature, these systems will lose their topological characteristics,which leads to the fact that coded information can be destructed by local errors.Therefore, topological ordered systems are fragile under thermal fluctuation. With this in mind, studying variation of topological entanglement entropy in terms of temperature, the vanishing of topological entanglement entropy would be seen, which shows the destruction of topological characteristics in system. In this thesis, we first introduced topological Kitaev model, and then the fragility of this topological system in terms of temperature has been studied
  9. Keywords:
  10. Topological Order ; Kitaev-Ising Model ; Topological Entanglement Entropy ; Thermal Fragility

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