Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality

Abstract

We study the role of electron-electron interactions near integer and abelian fractional quantum Hall (QH) transitions using composite fermion (CF) representations. Interaction effects are encapsulated in CF theories as gauge fluctuations. Without gauge fluctuations, the CF system realizes a `dual' representation of the non-interacting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $\theta -$term. While the transition is described by a strong-coupling fixed point of the NLSM, we are nevertheless able to deduce two of its properties. With $1/r$ interactions, 1) the transition has a dynamical exponent $z=1$, and 2) all transitions are `superuniversal': fractional and integer QH transitions are in the same universality class. With short-range interactions, $z=2$ and the fate of superuniversality remains unclear.

11 pages, 2 figures. Expanded version with pedagogical discussions and derivations

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• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Intrinsic (Axion) Statistical Topological Insulator
• Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect
• Quasi-exact ground-state algorithm for the random-field Potts model