Dissertation/Thesis Abstract

Investigating the topological order of an ansatz for the fractional quantum Hall effect in the half-filled second Landau level
by McCord, John J., M.S., California State University, Long Beach, 2016, 62; 10240257
Abstract (Summary)

The Moore-Read Pfaffian and anti-Pfaffian states have been under scrupulous review as candidates which describe the fractional quantum Hall effect at filling factor 5/2. Quantum states in the universality class of the Moore-Read Pfaffian/anti-Pfaffian have non-trivial intrinsic topological order and support low-energy non-Abelian excitations that have applications in fault-tolerant topological quantum computing schemes. Both states are exact ground states of three-body Hamiltonians that explicitly break particle-hole symmetry. We study the topological order of a competing ansatz state &PSgr;2 that is the exact ground state of a two-body Hamiltonian that preserves particle-hole symmetry. In particular, we calculate the bipartite entanglement entropy and spectra in the lowest Landau level in the spherical geometry for &PSgr; 2. We perform such calculations for a finite number of electrons up to 14. We then extrapolate to the thermodynamic limit the topological entanglement entropy γ as a measure of the topological order of the ansatz and compare to the known value of the Moore-Read Pfaffian/anti-Pfaffian state. We also study the orbital entanglement spectra for &PSgr;2 and compare with the Moore-Read Pfaffian and two-body Coulomb ground states. We show that our extrapolation of γ lies within the uncertainty of the known value of γ for the Moore-Read Pfaffian state, and that the orbital entanglement spectra of &PSgr;2 assumes a similar structure to that of the two-body Coulomb interaction.

Indexing (document details)
Advisor: Peterson, Michael R.
Commitee: Bill, Andreas, Kwon, Chuhee, Peterson, Michael R.
School: California State University, Long Beach
Department: Physics and Astronomy
School Location: United States -- California
Source: MAI 56/02M(E), Masters Abstracts International
Subjects: Condensed matter physics
Keywords: Ansatz, Filled, Fractional, Half-filled, Hall, Landau, Quantum, Topological
Publication Number: 10240257
ISBN: 9781369426816
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