ORCID

http://orcid.org/0000-0002-4681-059X

Date of Award

Spring 5-15-2023

Author's School

Graduate School of Arts and Sciences

Author's Department

Physics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

Systems confined in the two-dimensional world have long played a major role in physics. Under a quantizing magnetic field, these systems can exhibit phases of matter described by beautiful trial wave functions. Although there are numerous solvable models for fractional quantum Hall (FQH) physics, they are primarily developed and studied from the viewpoint of clustering properties of these wave functions in first quantization. Here we investigate frustration-free Hamiltonians of FQH states and their connection with 1D tensor networks, or matrix product state (MPS), based on the conformal field theory (CFT) representation of their ground and excited states. Examining these Hamiltonians on an orbital basis, which is the natural basis for the tensor network representation of FQH states, results in long-range frustration-free lattice models. The link between MPS-like states and frustration-free parent Hamiltonians is a central guiding principle for developing solvable lattice models. Nonetheless, this connection has only been established thus far for short-range Hamiltonians and MPSs with finite bond dimensions. Unlike other situations, the FQH scenario presents a distinctive circumstance. We demonstrate the direct relationship between the parent Hamiltonians of Laughlin states and their MPS structure with an infinite bond dimension; and utilize a comparable approach to show the connection between the non-Abelian Moore-Read states and their three-body parent Hamiltonian, with a particular emphasis on the Majorana modes and their implications for characterizing edge excitations.

In collaboration with experimentalists, we showcase measurements on the dispersion of optical transitions in the relativistic quantum Hall effect in dual-gated bilayer graphene alongside quantitative predictions. The exceptional electronic properties of bilayer graphene, such as massive chiral quasiparticles that create an octet of closely spaced energy levels under magnetic quantization, make it a prime candidate for exploring and testing models for interactions in this system. We employ the C2DEG theory to incorporate Coulomb interactions within the mean-field Hartree-Fock approximation. Additionally, we consider asymmetric interactions to characterize electron-electron and electron-phonon interactions in the presence of isospin anisotropy, regularization due to the infinitely deep sea of filled states, Zeeman interaction, and an external electric field. The energy levels are obtained self-consistently, using the screening factor and asymmetric interaction couplings the adjustable parameters. Our predictions demonstrate excellent consistency and good quantitative agreement with recent experimental observations.

Language

English (en)

Chair and Committee

Alexander Seidel

Committee Members

Renato Feres, Erik Henriksen, Zohar Nussinov, Li Yang,

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