Inhalt

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   Acknowledgments
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   Introduction
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   Introduction, motivation, and outline
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  The single-channel single-impurity Kondo model
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   The Kondo effect
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   The Hamiltonian of the single-channel single-impurity Kondo model
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   Relation between the Kondo model and the Anderson model
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  A minimal model for deposited magnetic atoms and molecules
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   The bilinear spin Hamiltonian for the description of an isolated magnetic molecule
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   A Kondo model for deposited magnetic atoms and molecules
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   Symmetry properties of the Hamiltonian
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   SU(2) isospin symmetry
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   SU(2) spin symmetry
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   Spinflip symmetry
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   Particle-hole symmetry
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   The Numerical Renormalization Group for the thermodynamics of the single-channel Kondo model
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   Overview of a Numerical Renormalization Group calculation
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  The Numerical Renormalization Group (NRG)
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   Transformation to a continuous energy representation
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   Transformation to a dimensionless representation
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   Example: One-dimensional tight-binding electrons
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  Logarithmic discretization I: Standard discretization with z-averaging
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   Logarithmic discretization of the continuum of electronic states
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   z-averaging ("interleaved method")
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   Logarithmic discretization II: Improved discretization by Campo & Oliveira
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  Excursus: Continuum result for the spectral density of the operator f_{0 \mu}
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   Spectral densities
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   One-electron spectral density of the ideal Fermi gas
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   Spectral density of f_{0 \mu}
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   Logarithmic discretization III: "Optimal" discretization by Žitko & Pruschke
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   Parameters of the logarithmically discretized Hamiltonian for a constant density of states
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   Tridiagonalization of the discretized Hamiltonian: Mapping to the "Wilson chain"
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   Derivation of recursion relations for the parameters of the Wilson chain
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   Iterative diagonalization of the Wilson chain, basis truncation, and Renormalization Group aspect
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   Iterative construction of the Wilson chain and rescaling of the truncated Hamiltonians
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   "Traditional" basis truncation
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   "Modern" basis truncation
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   Motivation for the energy-based truncation scheme
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   Renormalization Group aspect
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   Implementation of the iterative diagonalization
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   Creating a matrix representation using quantum numbers Q and M
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   Excursus: Transforming to the eigenbasis of the Hamiltonian
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   Calculating the matrix representations of the creation operators for the next step
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   Temperature in a NRG calculation
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   Assigning temperatures to the different steps of the iterative diagonalization
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  Calculation of thermodynamic observables
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   The concept of an "impurity contribution"
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   Definitions of the considered observables
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   Calculating impurity contributions
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   Calculating local observables: The impurity magnetization
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  Application: The single-impurity Kondo model in zero magnetic field
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   Complete screening of an impurity spin S=1/2
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   Kondo temperature, universality, and Fermi liquid theory
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   Comparison with the Bethe ansatz solution
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   Effect of additional potential scattering
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   Effect of exchange anisotropy
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   Underscreening of an impurity spin S>1/2
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   The single-channel single-impurity Kondo model with and without uniaxial anisotropy in non-zero magnetic field
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   The isotropic single-impurity Kondo model in non-zero magnetic field
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   Thermodynamics of an impurity spin S=1/2
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   Thermodynamics of an impurity spin S>1/2
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   The Bethe ansatz solution for the universal impurity contribution to the magnetization of the isotropic single-impurity Kondo model
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   The closed expressions for the zero-temperature impurity contribution to the magnetization
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   Asymptotic field dependencies of the zero-temperature impurity contribution to the magnetization
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   "Numerical Renormalization Group calculations of the magnetization of Kondo impurities with and without uniaxial anisotropy"
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   Abstract
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   Introduction
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  Model
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   Hamiltonian
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   Transformation to an energy representation
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  Method and observables
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   Method: NRG
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   Observables
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  Impurities with D=0
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   Field-dependence of the magnetization
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   Impurities with easy axis anisotropy
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   Field-dependence of the impurity magnetization
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   Impurity contribution to the magnetization and the susceptibility
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  Impurities with hard axis anisotropy
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   Magnetic field dependence of the impurity magnetization
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  Field-induced Kondo effects
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   Effective models near groundstate level crossings in the limit of arbitrarily large anisotropy
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   Magnetic field dependence of impurity contributions near effective level crossing fields
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   Temperature dependence of impurity contributions at effective level crossing fields
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   Properties of the effective model for vanishing electron g-factor
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   Comparison of anisotropy- and field-induced pseudo-spin-1/2 Kondo effect for half-integer impurity spin
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   Summary
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   Acknowledgments
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  Numerical Renormalization Group calculations with conduction electron Zeeman term
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   Logarithmic discretization
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   Tridiagonalization
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   Dependence of the zero-temperature magnetization on the coupling strength for D=0
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   Effect of the electron g-factor on M and the connection between M and M_{imp}
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   Technical details regarding the study of the effective model for vanishing electron g-factor
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   References
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   Summary
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   Appendix
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  Initialization of the iterative diagonalization of the Wilson chain
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   Analytical results for the eigensystem and certain matrix elements of a truncated Wilson chain comprising a spin-1/2 impurity and the zeroth lattice site
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   Encoding, manipulating, and creating product basis states of the Wilson chain
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   Encoding and manipulating product basis states
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   Creating a product basis subject to constraints
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   Bibliography