Towards a theory of topological phases in quantum Hall systems: the pattern of zeros approach

Maissam Barkeshli, MIT.

Abstract: The theory of the fractional quantum Hall (FQH) states relies on the use of model wave functions and ideal Hamiltonians to characterize the different possible topological phases and their topological excitations. The pattern of zeros approach is an attempt to characterize these wave functions by the order of their zeros as various numbers of particles are brought together. Such an approach allows us to quantitatively characterize and systematically classify FQH ground state wave functions and their topological excitations. This leads to the construction of new non-Abelian wave functions for both single-layer and multilayer FQH systems and to a further understanding of the structure of the quasiparticles in the FQH states.