PhD Thesis - Universität Augsburg

More documents

Recommendations

Info

Erstgutachter: Zweitgutachter: Prof. Dr. Arno P. Kampf Prof. Dr. Thilo Kopp Tag der Einreichung: 17. Januar 2011 Tag der mündlichen Prüfung: 03. Juni 2011
Contents i CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 Model Hamiltonian for electrons in solids . . . . . . . . . . . . . . . . . . . 7 1.2 Hubbard model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 t-J and Heisenberg models . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Extended Hubbard models . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.1 Next-nearest neighbor interaction . . . . . . . . . . . . . . . . . . . 21 1.4.2 Peierls distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.3 Ionic potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2. Density-Matrix Renormalization Group . . . . . . . . . . . . . . . . . . . . . 23 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Matrix-Product State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.1 MPS, Blocks, and a Superblock . . . . . . . . . . . . . . . . . . . . 28 2.2.2 Operators in block effective basis . . . . . . . . . . . . . . . . . . . 30 2.3 Density-Matrix Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Infinite-System DMRG algorithm . . . . . . . . . . . . . . . . . . . . . . . 43 2.5 Finite-System DMRG algorithm . . . . . . . . . . . . . . . . . . . . . . . . 46 2.6 Implementation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6.1 Superblock Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . 51 2.6.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.6.3 Wave-function transformations . . . . . . . . . . . . . . . . . . . . . 55 2.6.4 Additive quantum numbers . . . . . . . . . . . . . . . . . . . . . . 57 3. Real-time evolution using DMRG . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Early attempts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3 Adaptive time-dependent DMRG . . . . . . . . . . . . . . . . . . . . . . . 68 3.4 Time-step targeting adaptive time-dependent DMRG . . . . . . . . . . . . 74 3.4.1 Performing time evolution . . . . . . . . . . . . . . . . . . . . . . . 75
Page 1: Phase Transitions and Real-Time Dyn
Page 6 and 7: ii Contents 3.4.2 Hilbert space ada
Page 9 and 10: Introduction 1 INTRODUCTION Theoret
Page 11 and 12: Introduction 3 transport can be cal
Page 13 and 14: Introduction 5 strongly correlated
Page 15 and 16: 7 1. MODELS As it is well known, a
Page 17 and 18: 1.1. Model Hamiltonian for electron
Page 19 and 20: 1.1. Model Hamiltonian for electron
Page 21 and 22: 1.2. Hubbard model 13 longer-ranged
Page 23 and 24: 1.2. Hubbard model 15 where (−1)
Page 25 and 26: 1.2. Hubbard model 17 ceptions are
Page 27 and 28: 1.3. t-J and Heisenberg models 19 2
Page 29 and 30: 1.4. Extended Hubbard models 21 neg
Page 31 and 32: 23 2. DENSITY-MATRIX RENORMALIZATIO
Page 33 and 34: 2.2. Matrix-Product State 25 access
Page 35 and 36: 2.2. Matrix-Product State 27 Note,
Page 37 and 38: 2.2. Matrix-Product State 29 where
Page 39 and 40: 2.2. Matrix-Product State 31 call L
Page 41 and 42: 2.3. Density-Matrix Projection 33 T
Page 43 and 44: 2.3. Density-Matrix Projection 35 o
Page 45 and 46: 2.3. Density-Matrix Projection 37 a
Page 47 and 48: 2.3. Density-Matrix Projection 39 t
Page 49 and 50: 2.3. Density-Matrix Projection 41 U
Page 51 and 52: 2.4. Infinite-System DMRG algorithm
Page 53 and 54: 2.4. Infinite-System DMRG algorithm
Page 55 and 56:
2.5. Finite-System DMRG algorithm 4
Page 57 and 58:
2.5. Finite-System DMRG algorithm 4
Page 59 and 60:
2.6. Implementation details 51 2.6.
Page 61 and 62:
2.6. Implementation details 53 wher
Page 63 and 64:
2.6. Implementation details 55 wher
Page 65 and 66:
2.6. Implementation details 57 Next
Page 67 and 68:
2.6. Implementation details 59 (a)
Page 69 and 70:
61 3. REAL-TIME EVOLUTION USING DMR
Page 71 and 72:
3.1. Introduction 63 the geometry o
Page 73 and 74:
3.2. Early attempts 65 - the system
Page 75 and 76:
3.2. Early attempts 67 (a) (b) Figu
Page 77 and 78:
3.3. Adaptive time-dependent DMRG 6
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
3.4. Time-step targeting adaptive t
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
3.5. Accuracy of adaptive time-depe
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
3.6. Conclusions 121 2.5 2 S vN (i,
Page 131 and 132:
123 4. NATURE OF THE BAND- TO MOTT-
Page 133 and 134:
4.1. Ionic Hubbard model 125 and no
Page 135 and 136:
4.1. Ionic Hubbard model 127 are gi
Page 137 and 138:
4.1. Ionic Hubbard model 129 Figure
Page 139 and 140:
4.1. Ionic Hubbard model 131 Figure
Page 141 and 142:
4.1. Ionic Hubbard model 133 0.4 0.
Page 143 and 144:
4.1. Ionic Hubbard model 135 〈S z
Page 145 and 146:
4.1. Ionic Hubbard model 137 0.12 0
Page 147 and 148:
4.2. Adiabatic Holstein-Hubbard mod
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
4.3. Conclusions 149 BI-MI transiti
Page 159 and 160:
151 5. REAL-TIME DYNAMICS OF SPIN A
Page 161 and 162:
5.1. One-dimensional Hubbard model
Page 163 and 164:
5.2. Computational setup 155 the el
Page 165 and 166:
5.3. Real-time evolution in the tig
Page 167 and 168:
5.4. Real-time evolution in the Hub
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
5.5. Ballistic vs. subdiffusive dyn
Page 187 and 188:
5.5. Ballistic vs. subdiffusive dyn
Page 189 and 190:
5.6. Conclusions 181 shows almost q
Page 191 and 192:
5.6. Conclusions 183 the spin pertu
Page 193 and 194:
185 6. SUMMARY AND OUTLOOK In this
Page 195 and 196:
187 phenomenon of spin-charge separ
Page 197 and 198:
spin-perturbation is ballistic in b
Page 199:
Appendices 191
Page 202 and 203:
194 Appendix A. Free Spinless Latti
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
206 Appendix B. Ionic-Chain Figure
Page 216 and 217:
208 Appendix B. Ionic-Chain equal t
Page 218 and 219:
210 Appendix B. Ionic-Chain The on-
Page 220 and 221:
212 Appendix B. Ionic-Chain (a) ∆
Page 222 and 223:
214 Appendix B. Ionic-Chain 〈n i
Page 224 and 225:
216 Appendix B. Ionic-Chain 〈n i
Page 226 and 227:
218 Appendix B. Ionic-Chain
Page 228 and 229:
220 Bibliography [12] Z. Bai, J. De
Page 230 and 231:
222 Bibliography [39] A. J. Daley,
Page 232 and 233:
224 Bibliography [65] A. E. Feiguin
Page 234 and 235:
226 Bibliography [92] M. C. Gutzwil
Page 236 and 237:
228 Bibliography [120] V. Hunyadi,
Page 238 and 239:
230 Bibliography [147] S. Langer, F
Page 240 and 241:
232 Bibliography [173] T. Mitani, Y
Page 242 and 243:
234 Bibliography [200] K. Rodriguez
Page 244 and 245:
236 Bibliography [227] H. Takasaki,
Page 246 and 247:
238 Bibliography [253] P. Werner, T
Page 248 and 249:
240 List of publications
Page 250:
242 Acknowledgments invariable moti
show all

PhD Thesis - Universität Augsburg

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?