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Continuous Matrix Product Ansatz for Studying 1+1 Quantum Field Theories

Vardian Zarrin Abadi, Niloofar | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51057 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Naseh, Ali
  7. Abstract:
  8. In the last decade, the developement of Quantum Information theory have created new concepts and methods in the study of quantum many-body systems, that previously weren’t available to physicist involved in areas such as condensed matter and field theory. One of the most important steps is the insight provided by structure of the many body system’s Hilbert space. Although, it is not completed, it leads us to deep results.In fact, we have found out that with high probability, the state of a many-body system is located in a very small corner of the Hilbert space, which requires only a small number of parameteres to describe it, that with respect to the number of particles, it grows linearly instead of exponentially. and this approach is a cornerstone of success in “ Density Matrix Renormalization Group” and “Matrix Product States” methods.Recently, the “Matrix Product States” method is generalized for estimation of the ground state of continuous systems and non-relativistic Quantum field theories.For instance,there is a good estimation for the ground state of Lieb-Lingir model.In this thesis, we study the sine-Gordon model by continuous Matrix Product states
  9. Keywords:
  10. Entanglement ; Density Matrix ; Entanglement Entropy ; Matrix Product State ; Variational Renormalization Groups ; Continuous Matrix Product States

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