請用此 Handle URI 來引用此文件：
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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝長澤 | zh_TW |
| dc.contributor.advisor | Chang-Tse Hsieh | en |
| dc.contributor.author | 陳柏豪 | zh_TW |
| dc.contributor.author | Bo-Hao Chen | en |
| dc.date.accessioned | 2025-08-18T00:52:50Z | - |
| dc.date.available | 2025-08-18 | - |
| dc.date.copyright | 2025-08-15 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-08-06 | - |
| dc.identifier.citation | [1] Kazuaki Takasan, Masaki Oshikawa, and Haruki Watanabe. Adiabatic transport in one-dimensional systems with a single defect, 2021.
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Entanglement spectrum and entropy in topological non-hermitian systems and nonunitary conformal field theory. Physical Review Research, 2(3), July 2020. [28] Michael H Freedman, Jan Gukelberger, Matthew B Hastings, Simon Trebst, Matthias Troyer, and Zhenghan Wang. Galois conjugates of topological phases. Physical Review B—Condensed Matter and Materials Physics, 85(4):045414, 2012. [29] Laurens Lootens, Robijn Vanhove, Jutho Haegeman, and Frank Verstraete. Galois conjugated tensor fusion categories and nonunitary conformal field theory. Physical review letters, 124(12):120601, 2020. [30] Sora Cho and Matthew P. A. Fisher. Criticality in the two-dimensional random-bond ising model. Phys. Rev. B, 55:1025–1031, Jan 1997. [31] Masaki Oshikawa and Ian Affleck. Boundary conformal field theory approach to the critical two-dimensional ising model with a defect line. Nuclear Physics B, 495(3):533–582, 1997. [32] Gregory Moore and Nicholas Read. Nonabelions in the fractional quantum hall effect. 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Exact conformal-field-theory results on the multi-channel kondo effect: Asymptotic three-dimensional space- and timedependent multi-point and many-particle green’s functions. Nuclear Physics B, 428(3):545–611, 1994. [38] Ian Affleck. Conformal field theory approach to the kondo effect. arXiv preprint cond-mat/9512099, 1995. [39] C. L. Kane and Matthew P. A. Fisher. Transport in a one-channel luttinger liquid. Phys. Rev. Lett., 68:1220–1223, Feb 1992. [40] C. L. Kane and Matthew P. A. Fisher. Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas. Phys. Rev. B, 46:15233–15262, Dec 1992. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98560 | - |
| dc.description.abstract | 共形場論對描述臨界現象中的普適性行為提供了一套精確的分析框架，而邊界共形場論則在理解臨界系統中的量子雜質問題方面扮演重要的角色。另一方面，非厄米物理源於放寬厄米性條件，能有效刻畫具有增益、耗散與衰減等現象的開放量子系統的動力學。受這些發展的啟發，我們探討非么正邊界共形場論與非厄米量子雜質臨界系統之間的關聯。我們將邊界共形場論的框架擴展至包含非厄米雜質的情況，並利用折疊技巧將晶格模型中的雜質強度對應到一個有效的位勢參數，從而建立晶格散射矩陣與邊界共形場論黏合矩陣之間的對應關係。在此對應中，非厄米模型中機率守恆的違反體現在邊界共形場論中非么正的邊界條件。我們進一步顯示，晶格模型在費米點所產生的雜質能量位移，與邊界共形場論中基態能量的有限尺寸修正相符；該修正隨系統尺寸呈反比縮放，並由費米動量下的傳輸振幅所決定。這項結果推廣了對厄米雜質系統的既有研究成果，例如 [1,2] 中所提出的。總結而言，我們的研究表明，邊界共形場論的技術可以有效應用於非厄米量子雜質問題的分析，為非厄米性與邊界或缺陷臨界性之間的關係提供了新的見解。 | zh_TW |
| dc.description.abstract | Conformal field theory (CFT) offers an exact analytical framework for describing the universal features of critical phenomena, while boundary conformal field theory (BCFT) plays a central role in understanding quantum impurity problems at criticality. Meanwhile, non-Hermitian physics, which arises from relaxing the Hermiticity condition, effectively captures the dynamics of open quantum systems with gain, loss, and decay. Motivated by these developments, we explore the connection between non-unitary BCFT and non-Hermitian quantum impurity critical systems. Extending the BCFT framework to include non-Hermitian impurities, we map the lattice impurity strength to an effective barrier parameter using the folding trick, establishing a direct correspondence between the lattice scattering matrix and the BCFT gluing matrix. In this correspondence, the violation of probability conservation in the non-Hermitian model manifests as non-unitary boundary conditions in BCFT. We further show that the impurity-induced energy shift at the Fermi point(s) in the lattice model matches the finite-size correction to the ground-state energy in BCFT, which scales inversely with the system size and is determined by the transmission amplitude at the Fermi momentum. This extends the known results for Hermitian impurity systems, e.g., presented in [1,2]. Our results demonstrate that BCFT techniques can be fruitfully applied to the study of non-Hermitian quantum impurity problems, providing new insights into the interplay between non-Hermiticity and boundary or defect criticality. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-08-18T00:52:50Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-08-18T00:52:50Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Denotation xvii Chapter 1 Introduction 1 1.1 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Overview of Thesis Structure . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Non-Hermitian Physics 5 2.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Non-Hermitian Quantum Mechanics . . . . . . . . . . . . . . . . . 6 2.1.2 PT-symmetry and Real Spectra . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Exceptional Points . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Experimental Realizations and Applications . . . . . . . . . . . . . . 12 2.3 Relation to non-unitary Conformal Field Theory . . . . . . . . . . . 13 2.4 Challenges and Open Questions . . . . . . . . . . . . . . . . . . . . 14 Chapter 3 Conformal Field Theory Techniques 15 3.1 Brief introduction of CFT . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.1 Definition of Conformal Transformations . . . . . . . . . . . . . . 16 3.1.2 Witt Algebra and Virasoro Algebra . . . . . . . . . . . . . . . . . . 17 3.1.3 Operator Product Expansion (OPE) . . . . . . . . . . . . . . . . . . 20 3.1.4 Scaling Behavior and Critical Exponents . . . . . . . . . . . . . . . 21 3.2 Boundary Conformal Field Theory . . . . . . . . . . . . . . . . . . . 22 3.3 Boundary sine-Gordon model . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 Fermionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3.2 Partition Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Chapter 4 Non-Hermitian Critical Systems with Impurities and BCFT 33 4.1 Single Defect Models . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2 Scattering Matrix (S-matrix) Formalism . . . . . . . . . . . . . . . . 35 4.2.1 Connection to Transport Properties . . . . . . . . . . . . . . . . . . 36 4.2.2 S-matrix with Hermiticity . . . . . . . . . . . . . . . . . . . . . . . 37 4.2.3 Generalize to non-Hermitian case . . . . . . . . . . . . . . . . . . . 38 4.2.4 Critical Point Behavior . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Correspondence with BCFT . . . . . . . . . . . . . . . . . . . . . . 42 4.3.1 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3.2 Folding Trick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3.3 Dependence of Boundary Coupling on Lattice Parameter . . . . . . 48 4.3.4 Dirichlet Boundary Condition . . . . . . . . . . . . . . . . . . . . . 49 4.3.5 Neumann Boundary Condition . . . . . . . . . . . . . . . . . . . . 51 4.4 Unitarity, Hermiticity, and Their Violations . . . . . . . . . . . . . . 52 4.4.1 Hermiticity in the Lattice Model . . . . . . . . . . . . . . . . . . . 53 4.4.2 Unitarity Condition of the Gluing Matrix . . . . . . . . . . . . . . . 54 4.4.3 Equivalence of Unitarity and Hermiticity . . . . . . . . . . . . . . . 55 4.5 Ground State Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.5.1 Eigenvalues of S-matrix . . . . . . . . . . . . . . . . . . . . . . . . 59 4.5.2 Quantization Condition . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5.3 Energy Spectrum Expansion . . . . . . . . . . . . . . . . . . . . . 62 4.5.4 Matching Finite-Size Corrections to BCFT Predictions . . . . . . . 66 4.6 Excited State Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.6.1 Excitations by Raising N Levels . . . . . . . . . . . . . . . . . . . 69 4.6.2 Excitations by Adding or Removing Q Particles . . . . . . . . . . . 72 4.6.3 Correspondence Between Excitation Energies and BCFT Spectrum . 75 4.7 Physical Implications and Interpretation . . . . . . . . . . . . . . . . 79 Chapter 5 Discussion and Conclusion 81 5.1 Summary of Major Results . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Potential Future Directions . . . . . . . . . . . . . . . . . . . . . . . 82 5.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 83 References 85 Appendix A — Virasoro algebra 91 A.1 The Witt Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 A.2 Central Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 A.3 Correlation Functions and Operator Product Expansion (OPE) . . . . 93 Appendix B — Unitarity Check of Gluing Matrix 99 Appendix C — Expansion and Correction of qn 101 | - |
| dc.language.iso | en | - |
| dc.subject | 邊界共形場論 | zh_TW |
| dc.subject | 共形場論 | zh_TW |
| dc.subject | 散射矩陣 | zh_TW |
| dc.subject | 缺陷 | zh_TW |
| dc.subject | 非厄米 | zh_TW |
| dc.subject | non-Hermitian | en |
| dc.subject | Impurity | en |
| dc.subject | S-matrix | en |
| dc.subject | Boundary Conformal Field Theory | en |
| dc.subject | Conformal Field Theory | en |
| dc.title | 單缺陷非厄米系統與邊界共形場論 | zh_TW |
| dc.title | Single Impurity non-Hermitian System and Boundary Conformal Field Theory | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳俊瑋;沈家賢;任祥華 | zh_TW |
| dc.contributor.oralexamcommittee | Jiunn-Wei Chen;Chia-Hsien Shen;Hsiang-Hua Jen | en |
| dc.subject.keyword | 共形場論,邊界共形場論,非厄米,缺陷,散射矩陣, | zh_TW |
| dc.subject.keyword | Conformal Field Theory,Boundary Conformal Field Theory,non-Hermitian,Impurity,S-matrix, | en |
| dc.relation.page | 102 | - |
| dc.identifier.doi | 10.6342/NTU202501665 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-08-10 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| dc.date.embargo-lift | 2025-08-18 | - |
| 顯示於系所單位： | 物理學系 | |
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