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A Study of the Phase Diagram of the Hubbard Model Using Modern Numerical Methods

Manavi, Alireza | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53668 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Vaezi, Mir Abolhassan
  7. Abstract:
  8. The Hubbard model is one of the simplest interacting models in theoretical physics, especially condensed matter physics which despite its simplicity, its solutions are highly nontrivial and intractable. After 5 decades since its introduction, its phase diagram is not fully understood and whether or not, it has a high-temperature superconducting phase. In this thesis, we aim to employ the recent advances in machine learning and GPU programming to accelerate the QMC method. By accelerated QMC methods, we can explore the Hubbard model's phase diagram more efficiently. Using massive parallelization of the GPUs can speed up the measuring process by several times. The self-learning quantum Monte-Carlo is a general approach for quantum models, which has recently been used for solving many-body problems. This method reduces the QMC algorithm's complexity and decreases the auto-correlation time near the critical point. It is based on finding an effective free energy functional with the help of machine learning techniques and utilizing it to predict the acceptance ratio of the Metropolis-Hasting algorithm. The main challenge of the QMC method is the sign problem. Using the self-learning quantum Monte-Carlo and GPU implementation of the DQMC method, we could increase the measuring rate. This can help us accessing lower temperatures
  9. Keywords:
  10. High Temperature Superconductor ; Quantum Monte Carlo Method ; Graphics Procssing Unit (GPU) ; Hubbard Model Phase Diagram ; Self-Learning Quantum Monte-Carlo

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