PhD Thesis - Universität Augsburg

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ii Contents 3.4.2 Hilbert space adaption strategy . . . . . . . . . . . . . . . . . . . . 78 3.4.3 Time-step targeting adaptive time-dependent DMRG based on the Krylov-subspace methods for the time-evolution . . . . . . . . . . . 81 3.5 Accuracy of adaptive time-dependent DMRG . . . . . . . . . . . . . . . . . 85 3.5.1 t-DMRG based on the Suzuki-Trotter time-evolution scheme . . . . 89 3.5.1.1 Analytical estimates . . . . . . . . . . . . . . . . . . . . . 89 3.5.1.2 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . 92 3.5.2 t-DMRG based on the Arnoldi method for the time-evolution . . . 113 3.5.3 Comparison and summary . . . . . . . . . . . . . . . . . . . . . . . 118 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4. Nature of the Band- to Mott-insulator transition in one-dimension . . . . 123 4.1 Ionic Hubbard model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.1.2 Symmetry analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.1.3 Exact diagonalization results . . . . . . . . . . . . . . . . . . . . . . 128 4.1.4 DMRG results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.1.4.1 Excitation gaps . . . . . . . . . . . . . . . . . . . . . . . . 129 4.1.4.2 Correlation functions . . . . . . . . . . . . . . . . . . . . . 133 4.2 Adiabatic Holstein-Hubbard model . . . . . . . . . . . . . . . . . . . . . . 139 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.2.2 Theoretical models . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.2.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.2.3.1 Charge- and spin-structure factors . . . . . . . . . . . . . 140 4.2.3.2 Optical response . . . . . . . . . . . . . . . . . . . . . . . 142 4.2.4 Phase diagram in the adiabatic limit . . . . . . . . . . . . . . . . . 143 4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5. Real-time Dynamics of Spin and Charge Densities in the One-dimensional Hubbard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.1 One-dimensional Hubbard model . . . . . . . . . . . . . . . . . . . . . . . 151 5.2 Computational setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.2.1 Preparation of the initial state . . . . . . . . . . . . . . . . . . . . . 155 5.2.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.2.3 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.3 Real-time evolution in the tight-binding model . . . . . . . . . . . . . . . . 157 5.4 Real-time evolution in the Hubbard model . . . . . . . . . . . . . . . . . . 159 5.4.1 System at half-filling . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5.4.2 System close to half-filling . . . . . . . . . . . . . . . . . . . . . . . 170
Contents iii 5.5 Ballistic vs. subdiffusive dynamics . . . . . . . . . . . . . . . . . . . . . . . 177 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6. Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 A. Free Spinless Lattice Fermions in One-Dimension . . . . . . . . . . . . . . . 193 A.1 Time evolution of a wave packet . . . . . . . . . . . . . . . . . . . . . . . . 195 A.2 Time evolution of Fock states . . . . . . . . . . . . . . . . . . . . . . . . . 202 B. Ionic-Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 List of publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Page 1: Phase Transitions and Real-Time Dyn
Page 4 and 5: Erstgutachter: Zweitgutachter: Prof
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
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Page 21 and 22: 1.2. Hubbard model 13 longer-ranged
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Page 27 and 28: 1.3. t-J and Heisenberg models 19 2
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2.6. Implementation details 51 2.6.
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2.6. Implementation details 53 wher
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2.6. Implementation details 59 (a)
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61 3. REAL-TIME EVOLUTION USING DMR
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3.1. Introduction 63 the geometry o
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3.2. Early attempts 65 - the system
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123 4. NATURE OF THE BAND- TO MOTT-
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4.1. Ionic Hubbard model 125 and no
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4.1. Ionic Hubbard model 127 are gi
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4.1. Ionic Hubbard model 129 Figure
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4.1. Ionic Hubbard model 131 Figure
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4.1. Ionic Hubbard model 133 0.4 0.
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4.1. Ionic Hubbard model 135 〈S z
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4.3. Conclusions 149 BI-MI transiti
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151 5. REAL-TIME DYNAMICS OF SPIN A
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5.2. Computational setup 155 the el
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5.6. Conclusions 181 shows almost q
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5.6. Conclusions 183 the spin pertu
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185 6. SUMMARY AND OUTLOOK In this
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187 phenomenon of spin-charge separ
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spin-perturbation is ballistic in b
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Appendices 191
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194 Appendix A. Free Spinless Latti
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206 Appendix B. Ionic-Chain Figure
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208 Appendix B. Ionic-Chain equal t
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210 Appendix B. Ionic-Chain The on-
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212 Appendix B. Ionic-Chain (a) ∆
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214 Appendix B. Ionic-Chain 〈n i
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216 Appendix B. Ionic-Chain 〈n i
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218 Appendix B. Ionic-Chain
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220 Bibliography [12] Z. Bai, J. De
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222 Bibliography [39] A. J. Daley,
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224 Bibliography [65] A. E. Feiguin
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226 Bibliography [92] M. C. Gutzwil
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228 Bibliography [120] V. Hunyadi,
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230 Bibliography [147] S. Langer, F
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232 Bibliography [173] T. Mitani, Y
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234 Bibliography [200] K. Rodriguez
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236 Bibliography [227] H. Takasaki,
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238 Bibliography [253] P. Werner, T
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240 List of publications
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242 Acknowledgments invariable moti
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PhD Thesis - Universität Augsburg

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