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Date of Award
Doctor of Philosophy (PhD)
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.
Chair and Committee
Zohar Nussinov, Michael Ogilvie, Xiang Tang, Li Yang
Chen, Li, "The Second Quantized Approach to the Study of Model Hamiltonians in Quantum Hall Regime" (2016). Arts & Sciences Electronic Theses and Dissertations. 985.
Available for download on Tuesday, December 15, 2116