Numerical Renormalization Group Calculations for Impurity ...

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Erstgutachter: Zweitgutachter: Priv. Doz. Dr. Ralf Bulla Prof. Dr. Thilo Kopp Tag der mündlichen Prüfung: 12. Januar 2007
i ACKNOWLEDGMENTS I would like to express my gratitude to my supervisor Priv.-Doz. Dr. Ralf Bulla, who gave me the opportunity to learn many excellent physics in leading scientific circumstances. It was a great pleasure to study the fascinating subjects of quantum impurity systems and quantum phase transitions by the non-perturbative method of numerical renormalization group. Moreover, I deeply appreciate his attentive guidance in all matters of scientific life. I wish to thank for the opportunity to join his collaboration with Professor Dr. Matthias Vojta in Köln, to whom I am greatly indebted for the works that are presented in the thesis. I would like to thank Professor Dr. Thilo Kopp for his willingness to co-report on the thesis. To Professor Dr. Dieter Vollhardt and Professor Dr. Arno P. Kampf, I return my gratitude for their stimulating encouragement and warm hospitality. I would like to give my sincere thanks to Dr. Sabine Tornow, Dr. Tae- Hyoung Gimm, and Professor Dr. Ning-Hua Tong for their invaluable help and collaboration. I owe many thanks to the senior colleagues, Dr. Unjong Yu, Dr. Sanjeev Kumar, Dr. Marcus Kollar, Dr. Krzysztof Byczuk, and Dr. Jan Kunes, who were willing to give their scientific advice and many words of comfort. To Martin Eckstein, Andreas Hackl, Robert Hager, Markus Schmid, Michael Sekania, Michael Sentef, Dr. Xinguo Ren, Dr. Ivan Leonov, Dr. Dmitry Lobaskin, and Dr. Georg Keller, I would like to thank for all kindness and cordialities that they showed. I wish to thank Mrs. Barbara Besslich and Mrs. Anita Seidl, who gave help in organizational matters with great tenderness. I owe particular thanks to Dr. Unjong Yu, Dr. Sanjeev Kumar, and Dr. Sabine Tornow for proofreading. At last, I would like to thank God for his guidance.
Page 1: Numerical Renormalization Group Cal
Page 6 and 7: iv Contents 6.2.3 Quantum critical
Page 8 and 9: 2 1. Overview in Chapter 6 indicate
Page 10 and 11: 4 2. Introduction to Quantum Phase
Page 22 and 23: 16 3. Numerical Renormalization Gro
Page 38 and 39: 32 4. Soft-Gap Anderson Model 0.06
Page 40 and 41: 34 4. Soft-Gap Anderson Model model
Page 42 and 43: 36 4. Soft-Gap Anderson Model 4.0 3
Page 44 and 45: 38 4. Soft-Gap Anderson Model 0 1 2
Page 46 and 47: 40 4. Soft-Gap Anderson Model r and
Page 48 and 49: 42 4. Soft-Gap Anderson Model ; see
Page 50 and 51: 44 4. Soft-Gap Anderson Model 1.5 1
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46 4. Soft-Gap Anderson Model Eq. (
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48 4. Soft-Gap Anderson Model
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50 5. Spin-Boson Model compared to
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52 5. Spin-Boson Model α c 1.2 0.8
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54 5. Spin-Boson Model 4 α=0.01 α
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56 5. Spin-Boson Model s=0.8. ∆=0
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58 5. Spin-Boson Model 1 QCP D E N
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60 5. Spin-Boson Model
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62 6. Bosonic Single-Impurity Ander
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'& &' '& '& &' '&
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78 7. Summary as the most important
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81 A. FIXED-POINTS ANALYSIS: SOFT-G
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A.1. Local moment fixed points 83
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A.1. Local moment fixed points 85 a
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A.1. Local moment fixed points 87 3
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A.1. Local moment fixed points 89 C
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A.2. Details of the Perturbative An
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97 B. THERMODYNAMICS IN THE OHMIC S
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99 0.8 0.6 a S imp (T) 0.4 0.2 α=1
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1/2. The agreement with the exact r
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103 C. BEC OF AN IDEAL BOSONIC GAS
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105 D. DETAILS ABOUT THE ITERATIVE
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Bibliography 107 BIBLIOGRAPHY Affle
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Bibliography 109 Georges, A., Kotli
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Bibliography 111 Vojta, M. and Frit
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CURRICULUM VITAE Name: Hyun-Jung Le
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LIST OF PUBLICATIONS [1] H.-J. Lee
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