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Title:  New perspectives on fractional quantum Hall physics 
Author(s):  Sohal, Ramanjit 
Director of Research:  Fradkin, Eduardo 
Doctoral Committee Chair(s):  Stone, Michael 
Doctoral Committee Member(s):  Madhavan, Vidya; Gadway, Bryce 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  quantum Hall effect
fractional Chern insulators topological order field theory dualities entanglement entropy 
Abstract:  Despite having been discovered nearly four decades ago, fractional quantum Hall (FQH) states continue to provide platforms for the discovery of novel physical phenomena. In this thesis, I present a study of these remarkable phases of matter from three perspectives: (1) the role of an underlying lattice and its symmetries in engendering novel FQH states, (2) the description of nonAbelian FQH states using recently developed field theory dualities, and (3) the use of entanglement entropy in characterizing interfaces of FQH states. In the first part, we examine phases of matter known as fractional Chern insulators (FCIs), lattice analogues of FQH states. We begin in Chapter 2 by formulating a composite fermion theory for FCI states in a kagome lattice model, making use of a recently developed lattice ChernSimons theory to effect the flux attachment. We identify sequences of Abelian states, including states for which the Hall conductance does not match the filling fraction, which we characterize as realizing distinct translational symmetry fractionalization classes. Next, we apply this formalism in Chapter 3 to identify paired states of composite fermions in a squarelattice Hofstadter model. Magnetic translation symmetry is found to enforce finitemomentum pairing of the composite fermions, yielding pairdensity wave (PDW) states with daughter chargedensity wave order, analogous to the PDWs conjectured to describe the highT c cuprate superconductors. This constitutes a novel example of intertwined orders, in which topological order and broken symmetry order arise from a common microscopic origin. In the second part, we apply a recently proposed web of ChernSimonsmatter theory dualities to develop effective field theories for a large class of nonAbelian FQH states. First, in Chapter 4, we demonstrate how these dualities can be used to construct bosonic LandauGinzburg theories of the ReadRezayi and generalized nonAbelian spin singlet states by introducing interlayer interactions in a multilayer Abelian FQH system. Next, we extend this construction in Chapter 5 to develop a field theory and motivate a trial wave function for the elusive Fibonacci FQH state, which is the minimal model for realizing a universal topological quantum computer. We subsequently examine in Chapter 6 dual fermionic nonAbelian ChernSimonsmatter theories, allowing us to develop composite fermion descriptions of the BlokWen FQH states and a series of states which may be understood as arising from pairing in a dual Abelian composite fermion theory. Our analysis reveals that dual fermionic theories can predict distinct ground states in a magnetic field, demonstrating the utility of dualities in mapping out regions of the phase diagram of electrons at fractional filling. In the final part of this thesis, which comprises Chapter 7, we characterize interfaces of nonAbelian MooreRead FQH states using entanglement entropy. We first employ a cutandglue approach to obtain the expected topological entanglement entropy (TEE) for a uniform MooreRead state on the torus in each topological sector. This involves approximating the entanglement as arising purely from the coupled 1D chiral edge degrees of freedom at the entanglement cut. We next consider interfaces of distinct generalized MooreRead states, identify when the interfaces can be gapped using an anyon condensation picture, construct explicit gapping interactions, and then compute the TEE for an entanglement cut along the interface. It is found that the value of the TEE is related to the total quantum dimension of a “parent” topological phase of the two generalized MooreRead states between which the interface is formed. 
Issue Date:  20210615 
Type:  Thesis 
URI:  http://hdl.handle.net/2142/113123 
Rights Information:  Copyright 2021 Ramanjit Sohal 
Date Available in IDEALS:  20220112 
Date Deposited:  202108 
This item appears in the following Collection(s)

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