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Investigating the Second Quantization Form of the Entanglement Hamiltonian of the Hubbard Model and the Validity of the Local Temperature Ansatz

Pourjafarabadi, Mahdieh | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53457 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Vaezi, Mir Abolhassan
  7. Abstract:
  8. The Hamiltonian of the Hubbard model was introduced by Hubbard in 1963 to model electron correlations in narrow energy bands and it provided an approximate description of electrons in solids.This model provides a simple description of materials, but its exact solution is possible only in one dimension.In the physical examining of this model in quasi two-dimensional systems, the Density Matrix Renormalization Group(DMRG) is used, which is one of the most powerful numerical methods in studying quantum systems. The quantity that is important to solve the systems is the density matrix, which by knowing, many of the observable quantities of the systems can be obtained. Calculating the density matrix of a small part of the system by using DMRG requires solving a larger system, which is significantly time demanding. One of the methods in calculating the density matrix is to obtain the entanglement Hamiltonian of that part. In many cases, the entanglement Hamiltonian has no special simplified form and its analytical solution depends on the existence of special conditions in the system. This thesis is aimed to study the second quantization form of the quasi two-dimensional Hubbard model by using DMRG for the first time. Then, by comparing the results of this study with the local temperature ansatz, the validity of this hypothesis would be evaluated and then the locality of the entanglement Hamiltonian terms will be specified. In this study, we realized that the main terms in entanglement Hamiltonian are the same as the Hubbard Hamiltonian’s and the coefficients of these terms vary according to the distance from the separating boundary of the subsystems. To increase the accuracy in calculating the entanglement Hamiltonian we just need to consider higher order terms only near the separating boundary of the subsystems, and then we will also find out that the coefficients of non-local sentences are very small. By using the obtained entanglement Hamiltonian , many features of a system can be obtained without solving the entire system. This study can lead to the design of more efficient methods than the conventional DMRG
  9. Keywords:
  10. Hubbard Model ; Entanglement Hamiltonian ; Density Matrix Renormalization Group ; Second Quantization ; Local Temperature Ansatz

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