# "Physical Principles Underlying the Fractional Quantum Hall Effect"

Fri, 03/07/2014 - 14:00

Professor Juerg Froelich, Institute for Advanced Study

I
review an approach to the theory of the Quantum Hall Effect (QHE)
somewhat analogous to Landau's theory of phase transitions. After a
short recapitulation of some of the discoveries leading to the QHE, I
describe some of the main experimental facts and data and speculate
about possible applications. I then recall the basic equations of the
electrodynamics of incompressible Hall fluids (IHF). Among other things,
these equations imply the existence of chiral edge currents and
elucidate their relation to the 2D chiral anomaly, and they enable us to
determine the effective action of an IHF. The effectiveaction
constrains the large-scale quantum theory of an IHF, which I then study
in terms of conserved current densities. This leads to a transparent
understanding of the "quantization" of the Hall conductivity and enables
one to give a list of possible values of the Hall conductivity that
compares well with experimental data. If time permitsI also describe the
quantum theory of the edge degrees of freedom of an IHF and then sketch
some general ideas underlying my approach that have found interesting
applications to, e.g., the theory of topological insulators.

Towne 337