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Protection of the Topological Edge Quantum Order in A Spin Chain with Cluster Interactions and Coupled to Fermions

Mohseni Rajaee, Mazdak | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57722 (04)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. Out-of-equilibrium systems have garnered increasing interest in recent years. These many-body systems do not exhibit ergodic behavior, even in the presence of generic interactions, allowing locally stored quantum information to remain accessible for extended periods through local observables. Due to these exotic characteristics, such systems are ideal candidates for the realization of quantum computing. Many-body localized systems serve as a prime example of these non-ergodic systems. In the absence of thermalization, long-range quantum order can persist even in highly excited states, contrasting with thermal systems where long-range order can only exist in the ground state of gapped Hamiltonians. In this thesis, we begin with a review of basic concepts and then explore how many-body localization occurs in interacting systems. Furthermore, we examine how many body localization can protect long-range quantum order. Finally, we introduce a clean cluster spin chain with symmetry-protected topological order, coupled to fully interacting spinless fermions, demonstrating that the fermionic subsystem is many-body localized due to the topological properties of the cluster chain. We investigate the effect of many-body localization on the edge modes of the cluster chain, showing that despite the thermalization of the cluster chain, its edge modes are protected due to their coupling to localized fermions
  9. Keywords:
  10. Out-of-Equilibrium Phases ; Many Body Localization ; Quantum Order ; Symmetry Protected Topological Order ; Fermions ; Spin Chain

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