표제지
초록
Abstract
목차
1. 서론 9
1.1. Overview 9
1.2. Hubbard model 12
1.2.1. Site indexing 12
1.2.2. Hubbard Hamiltonian 14
1.3. Hartree-Fock approximation 15
1.3.1. Mean-field approximation 15
1.3.2. Disorder potential 17
1.3.3. Self-consistent magnetic field 18
1.3.4. Matrix representation 20
1.3.5. Initial states 23
1.3.6. Self-consistent process 26
2. Symmetry protected zigzag graphene nanoribbon 28
2.1. Interacting zigzag graphene nanoribbon의 특성 28
2.2. Symmetry protected zigzag graphene nanoribbon의 energy band structure 32
2.3. Symmetry protected zigzag graphene nanoribbon의 site spins 33
2.4. Integer charge gap-edge states 35
3. Topologically ordered zigzag graphene nanoribbon 38
3.1. Spin-split energy spectrum of Mott-Anderson insulator 38
3.2. Topologically ordered zigzag graphene nanoribbon의 site spins 40
3.3. Fractional states 43
4. Topological entanglement entropy 46
4.1. Topological entanglement entropy의 정의 46
4.2. Reduced density matrix를 이용한 entanglement entropy의 계산 47
4.2.1. Reduced density matrix 47
4.2.2. Hartree-Fock reduced density matrix 48
4.3. Wilson loop 방법 51
4.4. Weak disorder regime에서 topological entanglement entropy 55
4.5. Strong disorder regime에서 topological entanglement entropy 56
참고문헌 60