Harvard Condensed Matter Theory Seminars

Ilya Gruzberg, University of Chicago

Critical wave functions, conformal invariance, and theories for quantum Hall transitions.

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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