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研究生： 朱奕豪
Jhu, Yi-Hao
論文名稱： Entanglement Entropy Spectrum in Honeycomb Lattice
指導教授： 陳柏中
Chen, Po-Chung
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 42
中文關鍵詞： 量子糾纏 、量子糾纏熵 、六角晶格 、邊界態
外文關鍵詞： Entanglement, Entanglement entropy, Honeycomb Lattice, Edge state
相關次數： 點閱：4  下載：0 
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    • In this thesis, we using the tight-binding anisotropic honeycomb lattice to investigate the zero-energy edge states and the bipartite entanglement for the total system at half filling and $T=0$ by the entanglement entropy spectrum. The zero-energy edge states for the system having two infinite and parallel bearded or zigzag edges are found to survive only when the the system with PBC has two Dirac points. On the contrary, there is no zero-energy edge state for the system having two infinite and parallel armchair edges. On the other hand, we numerically calculate the entanglement entropy spectrum of the system $A$ that has finite bearded edges on up and down and finite armchair edges on left and right. The maximal entangled states of the entanglement entropy spectrum are found to have one-to-one correspondence to the zero-energy edge states of the system $A$ with OBC which means we numerically proves the one-to-one coorespondence between the zero-energy edge states and the maximal entangled states even when the edge is finite. In addition, we also find the zero-energy edge state of the system with longer bearded edge can be created by combining the zero-energy edge states of the system with shorter bearded edge.

    1 Introduction 2 The model and methods 2.1 The modeling 2.2 The R vector of two bands model 2.2.1 De nition of R vector 2.2.2 R vectors for lattice model 2.2.3 R vector and the zero-energy edge state 2.2.4 The R vector for honeycomb lattice with bearded edges 2.3 Green matrix and the Green matrix Hamiltonian 2.3.1 The Green matrix 2.3.2 The Green matrix Hamiltonian 2.3.3 The Green matrix for honeycomb lattice 3 The zero-energy edge states of in nite edges 3.1 The R vectors for di erent edges 3.2 The existence for the zero-energy edge states 4 The zero-energy edge states and maximal entangled states 4.1 The entanglement entropy 4.2 The numerical result 4.3 Analysis 4.3.1 The system of Lx = 3 and Ly = 1 4.3.2 The systems of Lx > 3 and Ly = 1 4.3.3 Combine small Lx systems into large Lx system 5 Conclusion and Outlook

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