Exact Hamiltonian For The Fractional Quantum Hall States In A Lattice

Sumanta Bandyopadhyay, Department of Physics, Washington University
January 27, 2017 at 4:00 pm
204 Crow
Event Description 

We have studied a lattice model to provide exactly flat bands with non-trivial Chern numbers. These bands are formally identical with single particle Landau levels of continuum electrons with quenched kinetic energy. Our results generalize models that have been studied by Eliot Kapit and Erich Mueller [PRL 105, 215303 (2010)] to the case beyond the lowest Landau. In the presence of local bosonic interaction Hamiltonians and proper filling factor, ground states may be stabilized that have the exact same form as certain well known many-body fractional Hall trial state defined for the continuum case. For most cases, our results can be reproduced to good approximation with NN and NNN hopping only, which can be easily realized in experiment. Our model allows us to realize exactly quantum Hall model wave functions on a lattice that had not previously been considered in this context, notably states further down the hierarchy and new non-Abelian states. This work suggest an interesting pathway to development of quantum computing.