ORCID
https://orcid.org/0000-0002-4870-9065
Date of Award
Winter 12-15-2016
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
Abstract
The study of model Hamiltonians, whose exact ground states are well known quantum Hall states, have been investigated solely in the literature from the point of view of first quantized approach in the last few decades. However, a second quantized approach to such Hamiltonians has not been taken in the same measure. In this dissertation, we study Haldane pseudopotential, which is the parent Hamiltonian of 1/M Laughlin state, and Trugman-Kivelson pseudopotential, which is the parent Hamiltonian of 2/5 unprojected Jain state. We find that the study of these Hamiltonians in their second quantized forms not only reproduces all properties of their zero modes already known in first quantized approach, but also sheds lights on general studies of such structures of these Hamiltonians as frustration free lattice Hamiltonians.
Language
English (en)
Chair and Committee
Alexander Seidel
Committee Members
Zohar Nussinov, Michael Ogilvie, Xiang Tang, Li Yang
Recommended Citation
Chen, Li, "The Second Quantized Approach to the Study of Model Hamiltonians in Quantum Hall Regime" (2016). Arts & Sciences Electronic Theses and Dissertations. 985.
https://openscholarship.wustl.edu/art_sci_etds/985
Comments
Permanent URL: https://doi.org/10.7936/K7154FGF