This item is under embargo and not available online per the author's request. For access information, please visit


Date of Award

Winter 12-15-2016

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



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.


English (en)

Chair and Committee

Alexander Seidel

Committee Members

Zohar Nussinov, Michael Ogilvie, Xiang Tang, Li Yang


Permanent URL:

Available for download on Tuesday, December 15, 2116