Entanglement Hamiltonian of Interacting Systems and its Applications in the Study of Strongly Correlated Systems

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Najafzadeh Oskoui, Hanieh | 2020

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53432 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Vaezi, Mir Abolhassan
Abstract:
Recent advances in numerical computations in the field of strongly correlated systems have provided us to calculate the entanglement spectrum and the entanglement entropy for interacting systems. Calculating the explicit form of the entanglement Hamiltonian (a.k.a. the modular Hamiltonian) is considered as a difficult problem.In this dissertation, we intend to introduce a method and by means of the d ensity-matrix-renormalization-group algorithm to obtain for the first time the second quantization form of the entanglement Hamiltonian of interacting systems at zero temperature. We implement our method for one-dimensional Heisenberg spin chain and also Heisenberg model on a square lattice both with open boundary condition and periodic boundary condition. In each case, we study the behavior of the coefficients of he entanglement Hamiltonian as a function of the distance from the boundary and examine the validity of the Local Temperature Approximation
Keywords:
Heisenberg Model ; Zero Temperature ; Density Matrix Renormalization Group ; Local Temperature Approximation ; Entanglement Hamiltonian ; Strongly Correlated Systems