The quantum Hall effect in finite magnetic fields
In the theory of the Quantum Hall Effect it is often convenient to ignore terms in the Hamiltonian that scatter electrons between different Landau levels. This is equivalent to assuming the presence of an infinite magnetic field. This dissertation consists of three studies which move beyond this approximation. The first study considers the effects of including Landau level mixing on the structure of the quasiparticles and on the ground state correlation functions. By means of perturbation theory in the interactions and by using the Landau-Ginzburg theory it is shown that for Coulomb (1/r) interactions the asymptotic long distance behavior of the charge and current profiles of the quasiparticles and of the correlation functions becomes algebraic when Landau level mixing is in the infinite field limit. The quasiparticle charge in experimental geometries is not quantized as precisely as the Hall conductance. The long range of the quasiparticle current distribution makes the angular momentum of an isolated quasiparticle ill-defined and appears to rule out a spin-statistics connection in the Hall Effect. The second study is concerned with the Quantum Hall Effect at odd integer filling factors, and at [nu] = 1/3 and 1/5, in a parameter space characterized by an arbitrary ratio of the Zeeman gap to the typical interaction energy. The system is incompressible, even when the Zeeman gap vanishes. When the Zeeman gap is large they are microscopic but in the limit of a vanishing Zeeman gap they are Skyrmions. Exact asymptotic results for the size, spin and energy of these excitations at small Zeeman energies are presented. The last study examines the problem of rigorously defining the ultra-local interactions commonly employed in the study of the Hall Effect. Repulsive point interactions do not exist in the full Hilbert space of the system. For a model of interacting anyons with point interactions there are bound states in the two-body problem.
- Research Organization:
- California Univ., Los Angeles, CA (United States)
- OSTI ID:
- 7160196
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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