Mott-hubbard Metal-insulator Transition and Optical Conductivity in High Dimensions (Berichte Aus Der Physik)

Introduction......Page 11
1.1 Hubbard Model......Page 15
1.1.1 Solid State Theory for Crystals......Page 16
1.1.2 Electronic Lattice Models......Page 17
1.1.3 Wannier Representation......Page 18
1.1.4 One-band Hubbard Model......Page 19
1.2 Dynamical Mean-Field Theory......Page 21
1.2.1 Limit Z for Spin Models......Page 22
1.2.2 Limit Z for Fermions......Page 23
1.2.3 Simplifications for the Hubbard Model in Z......Page 25
1.3.1 Wick\'s Theorem for the Discretized Impurity Problem......Page 29
1.3.2 Monte Carlo Importance Sampling......Page 31
1.4 Maximum Entropy Method......Page 33
2 Lattice and Density of States......Page 37
2.1.1 Definitions and Analytical Considerations......Page 39
2.1.2 Numerical Results......Page 42
2.1.3 Magnetic Frustration and Asymmetry of the DOS......Page 48
2.2 Bethe Lattice, RPE, and Disorder......Page 49
2.2.1 Bethe Tree, Cayley Tree, and Husimi Cactus......Page 50
2.2.2 Renormalized Perturbation Expansion......Page 53
2.3 General Density of States in d=......Page 57
2.4 Redefinition of the Bethe Lattice......Page 63
2.4.1 Model in d=......Page 64
2.4.2 Truncating the Hopping Range......Page 67
2.4.3 Finite Dimensionality......Page 69
2.4.4 Application to Asymmetric Model DOS......Page 72
2.5 Conclusion......Page 74
3 Mott Metal-Insulator Transition in the d Hubbard Model......Page 77
3.1.1 Experiment......Page 78
3.1.2 Theory......Page 81
3.2.1 Transitions of First or Higher Order......Page 83
3.2.2 Convergence of Fixed Point Methods......Page 85
3.2.3 Observables......Page 86
3.3 Phase Diagram: Development until 1999......Page 89
3.4 Discussion of QMC Algorithms......Page 92
3.4.1 Fourier Transformation and Smoothing......Page 94
3.4.2 Overrelaxation and Sweeping Strategies......Page 99
3.4.3 Estimation of Errors......Page 100
3.4.4 Parallelization......Page 102
3.5.1 Choice of Observables and Extrapolation......Page 103
3.5.2 Properties of the Insulating Phase......Page 106
3.5.3 Internal Energy......Page 110
3.5.4 Coexistence Phase Diagram......Page 118
3.5.5 Double Occupancy......Page 123
3.6.1 Differential Equation for dUc/dT and Linearization......Page 131
3.6.2 Low-temperature Asymptotics of Uc(T)......Page 135
3.6.3 Full Phase Diagram......Page 141
3.6.4 Implications of Partial Frustration......Page 148
3.7 Landau Theory and Criticality......Page 152
3.7.1 Free Energy Functional for the Bethe Lattice......Page 153
3.7.2 Direct Evaluation of Free Energy Differences......Page 154
3.7.3 Critical Behavior Near the MIT......Page 156
3.8.1 Maximum Entropy Method for Spectral Functions......Page 165
3.8.2 Algorithmic Choices and Numerical Tests......Page 170
3.8.3 Numerical Results for the Bethe DOS......Page 176
3.9 Conclusion......Page 183
4 Optical Conductivity......Page 185
4.1 Definition and General Properties of the Optical Conductivity......Page 186
4.1.1 Connection between Conductivity and Reflectivity......Page 187
4.1.2 Optical f-sum Rules......Page 189
4.1.3 Experiments......Page 191
4.1.4 Impact of Electronic Model Abstractions......Page 193
4.2.1 Kubo Formalism in the Continuum......Page 196
4.2.2 Kubo Formalism on a Lattice......Page 198
4.2.3 General Confirmation of the f-sum Rule......Page 200
4.3 Optical Conductivity in the Limit d......Page 202
4.3.1 Optical Conductivity for the Hypercubic Lattice......Page 204
4.3.2 f-sum Rule within the DMFT......Page 205
4.3.3 f-sum Rule and General Dispersion Formalism......Page 207
4.4 Optical Conductivity for the Bethe Lattice......Page 208
4.4.1 Treelike Layout of the Bethe Lattice......Page 210
4.4.2 Single-Chain Stacked Bethe Lattice......Page 214
4.4.3 Periodically Stacked Lattices......Page 219
4.4.4 Offdiagonal Disorder......Page 221
4.4.5 General Dispersion Method......Page 223
4.5.1 Coherent versus Incoherent Transport in High Dimensions......Page 226
4.5.2 Optical Conductivity in Finite Dimensions......Page 229
4.5.3 Impact of Frustration by t-t\' Hopping......Page 232
4.6 QMC Results for the Bethe Lattice......Page 235
4.6.1 Numerical Procedure for QMC Data......Page 236
4.6.2 Results: Self-Energy on the Real Axis......Page 240
4.6.3 Results: Optical Conductivity......Page 244
4.7 Conclusion......Page 252
5 Realistic Modeling of Strongly Correlated Materials......Page 255
5.1 La1-xSrxTiO3......Page 256
5.2 DFT and LSDA......Page 259
5.3 LDA+DMFT......Page 261
5.4.1 Density of States and Photoemission Spectra......Page 265
5.4.2 Influence of Discretization Errors......Page 271
5.4.3 Optical Conductivity......Page 278
5.5 Conclusion......Page 286
Summary......Page 289
A.1 Extensions of the Hubbard Model......Page 291
A.2 Characterization of Generic Momenta......Page 294
A.3 DCA, CDMFT, and RDA......Page 296
B Hyperdiamond Lattice......Page 301
C Fourier-Transforming Imaginary-Time Green Functions......Page 307
D.1 Electromagnetic Interaction Hamiltonian and Choice of Gauge......Page 315
D.2 Linear Response Theory......Page 316
Bibliography......Page 318
Index......Page 319
List of Publications......Page 341
Curriculum Vitae......Page 343
Acknowledgements......Page 345