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Title:  A field theory for the fractional quantum Hall effect 
Author(s):  Lopez, Ana Maria 
Doctoral Committee Chair(s):  Fradkin, Eduardo H. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, Condensed Matter 
Abstract:  In this thesis we derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are understood as infrared stable fixed points, and the long distance, low energy properties of the system should be described exactly by this theory. We show the existence of an exact equivalence between a system of interacting electrons, and a system of fermions tightly bound to infinitesimal solenoids carrying a statistical magnetic flux. These are the fermionic ChernSimons gauge field theories. The transformed system can be studied using standard techniques of perturbation theory, because its ground state, at the mean field level, is nondegenerate and has a gap to all the excitations. The power of this theory resides in the fact that it allows for a systematic calculation of the properties of the FQHE states around a meanfield ground state which has a gap. We consider in detail the fluid states in which the meanfield theory replaces the statistical fluxes by an average statistical magnetic field, i.e., the Average Field Approximation. We calculate the electromagnetic response functions within the semiclassical approximation, and determine the spectrum of collective excitations. We derive the ground state wave function directly from the field theory, and, as expected, we find the Laughlin wave function for the states with filling fraction $\nu$ = ${1\over m}$. We show that the universal properties of the Laughlin wave functions are a consequence of general principles, i.e., incompressibility, and Galilean and gauge invariance, which determine the analytic structure of the equaltime density correlation functions at long distances. Finally, we generalize our approach to study the FQHE in doublelayer systems. 
Issue Date:  1994 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/19861 
Rights Information:  Copyright 1994 Lopez, Ana Maria 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9512468 
OCLC Identifier:  (UMI)AAI9512468 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics