@phdthesis{Bercx2014,
  author    = {Bercx, Martin Helmut},
  title     = {Numerical studies of heavy-fermion systems and correlated topological insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-116138},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {In this thesis, we investigate aspects of the physics of heavy-fermion systems and correlated topological insulators. We numerically solve the interacting Hamiltonians that model the physical systems using quantum Monte Carlo algorithms to access both ground-state and finite-temperature observables. Initially, we focus on the metamagnetic transition in the Kondo lattice model for heavy fermions. On the basis of the dynamical mean-field theory and the dynamical cluster approximation, our calculations point towards a continuous transition, where the signatures of metamagnetism are linked to a Lifshitz transition of heavy-fermion bands. In the second part of the thesis, we study various aspects of magnetic pi fluxes in the Kane-Mele-Hubbard model of a correlated topological insulator. We describe a numerical measurement of the topological index, based on the localized mid-gap states that are provided by pi flux insertions. Furthermore, we take advantage of the intrinsic spin degree of freedom of a pi flux to devise instances of interacting quantum spin systems. In the third part of the thesis, we introduce and characterize the Kane-Mele-Hubbard model on the pi flux honeycomb lattice. We place particular emphasis on the correlations effects along the one-dimensional boundary of the lattice and compare results from a bosonization study with finite-size quantum Monte Carlo simulations.},
  subject      = {Schwere-Fermionen-System},
  language  = {en}
}
@phdthesis{Martin2010,
  author    = {Martin, Lee C.},
  title     = {The Kondo Lattice Model: a Dynamical Cluster Approximation Approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-49446},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {We apply an antiferromagnetic symmetry breaking implementation of the dynamical cluster approximation (DCA) to investigate the two-dimensional hole-doped Kondo lattice model (KLM) with hopping \$t\$ and coupling \$J\$. The DCA is an approximation at the level of the self-energy. Short range correlations on a small cluster, which is self-consistently embedded in the remaining bath electrons of the system, are handled exactly whereas longer ranged spacial correlations are incorporated on a mean-field level. The dynamics of the system, however, are retained in full. The strong temporal nature of correlations in the KLM make the model particularly suitable to investigation with the DCA. Our precise DCA calculations of single particle spectral functions compare well with exact lattice QMC results at the particle-hole symmetric point. However, our DCA version, combined with a QMC cluster solver, also allows simulations away from particle-hole symmetry and has enabled us to map out the magnetic phase diagram of the model as a function of doping and coupling \$J/t\$. At half-filling, our results show that the linear behaviour of the quasi-particle gap at small values of \$J/t\$ is a direct consequence of particle-hole symmetry, which leads to nesting of the Fermi surface. Breaking the symmetry, by inclusion of a diagonal hopping term, results in a greatly reduced gap which appears to follow a Kondo scale. Upon doping, the magnetic phase observed at half-filling survives and ultimately gives way to a paramagnetic phase. Across this magnetic order-disorder transition, we track the topology of the Fermi surface. The phase diagram is composed of three distinct regions: Paramagnetic with {\it large} Fermi surface, in which the magnetic moments are included in the Luttinger sum rule, lightly antiferromagnetic with large Fermi surface topology, and strongly antiferromagnetic with {\it small} Fermi surface, where the magnetic moments drop out of the Luttinger volume. We draw on a mean-field Hamiltonian with order parameters for both magnetisation and Kondo screening as a tool for interpretation of our DCA results. Initial results for fixed coupling and doping but varying temperature are also presented, where the aim is look for signals of the energy scales in the system: the Kondo temperature \$T_{K}\$ for initial Kondo screening of the magnetic moments, the Neel temperature \$T_{N}\$ for antiferromagnetic ordering, a possible \$T^{*}\$ at which a reordering of the Fermi surface is observed, and finally, the formation of the coherent heavy fermion state at \$T_{coh}\$.},
  subject      = {Gittermodell},
  language  = {en}
}