Fractional Quantum Hall Effect: Non-Abelian Quasiholes and Fractional Chern Insulators

Abstract

This dissertation investigates two aspects of the fractional quantum Hall effect.

First, I study the quasiholes in certain fractional quantum Hall states that are promising candidates for the experimental realization of non-Abelian anyons. I apply the newly developed matrix product state technique to examine these exotic excitations, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. This provides the first microscopic verification for the Fibonacci nature of the Z3 Read-Rezayi quasiholes. I also present evidence for the failure of plasma screening in the non-unitary Gaffnian wave function.

Second, I discuss the so-called fractional Chern insulators. These strongly-correlated phases are stabilized by repulsive interactions between electrons in a topological Bloch band. They exhibit fractional quantum Hall effect at zero magnetic field, but also display features fundamentally distinct from their continuum counterparts. I will construct model wave functions for these lattice states, and explain their difference from the continuum analogues as a specially crafted set of boundary conditions.