Aspects of Strongly Correlated Electron Systems: Theories of Impurity Spins and Excitons in Mott-Hubbard Insulators.
Abstract
This thesis presents some new results in the theory of strongly correlated electron systems. In Part I, we investigate a number of cases of an impurity spin, S, coupled to a D-dimensional quantum antiferromagnetic (AFM) background. The qualitative behavior of the impurity susceptibility is shown to depend upon the sublattice symmetry of the coupling, whether S is integer or half-integer, and the spectral density of the low lying AFM excitations. When the AFM background is ordered we show that the appropriate model to consider is one of nonabelian spin-boson type. Within this model, we argue that the symmetrically coupled half-integer spin impurity retains a Curie divergence in its low temperature susceptibility for D >= 2. In the case of a D = 1 spin-1/2 AFM chain the sublattice symmetric impurity behaves in the same way as the Kondo spin in the two-channel Kondo model and thus has a non-Curie ln(T_*/T) divergent susceptibility. This latter case is investigated via bosonization at the Emery-Kivelson strong coupling line. In Part II we present results which indicate the existence of strongly bound particle-hole excitations below the edge of the upper Hubbard band in a single-band, large -U Hubbard model in two dimensions, at half-filling. The appearance of these "exciton" states is due to correlation effects between a vacancy and a doubly-occupied site induced by the antiferromagnetic background, in contrast to the conventional mechanism of exciton formation via long range Coulomb attraction. The exciton band has s-wave symmetry and thus, while not contributing to optical absorption, should nonetheless be observable in Raman scattering experiments. We argue that in the insulating parent compounds of the high temperature superconducting cuprates the correlation effects giving rise to the excitons are of the same order of magnitude as particle-hole attraction due to longer range Coulomb interactions.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 1993
- Bibcode:
- 1993PhDT.......213C
- Keywords:
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- Physics: Condensed Matter