Harvard Condensed Matter Theory Seminars
Wave functions at Anderson localization-delocalization (LD)
transitions are known to exhibit complicated scale-invariant
behavior best characterized by an infinite set of multifractal
exponents. In the first part of the talk I will report on a
recent study of multifractal spectra of critical wave functions
at various Andreson transitions, focusing on finite systems
with boundaries. For the integer quantum Hall transition these
spectra were conjectured to be exactly parabolic in a number of
proposals of critical field theories for the transition. Our
numerical results for the Chalker-Coddington network model
firmly rule out the exact parabolicity. In addition, we provide
an exact result for surface multifractal exponents for a
related LD critical point in the BDI (chiral orthogonal) class.
In the second part I will talk about work in progress where we
consider point contact conductances for network model and use
ideas of stochastic geometry (SLE and conformal restriction) to
study average transport properties at the spin (class C) and
integer (class A) quantum Hall critical points.
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