[Theta] renormalization, superuniversality, and electron-electron interactions in the theory of the quantum Hall effect

I. S. Burmistrov

Published Jan 1, 2006• 0 citations

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[Theta] renormalization, superuniversality, and electron-electron interactions in the theory of the quantum Hall effect

I. S. Burmistrov

Published Jan 1, 2006• 0 citations

OpenAlex

Related papers

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Prashant Kumar, P. A. Nosov, S. Raghu

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 noninteracting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $\ensuremath{\theta}\phantom{\rule{0.28em}{0ex}}\mathrm{term}$. 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.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 noninteracting QH transition. With gauge fluctuations, the system is governed by a gauged nonlinear sigma model (NLSM) with a $\ensuremath{\theta}\phantom{\rule{0.28em}{0ex}}\mathrm{term}$. 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.

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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.

Superuniversality and non-abelian bosonization in

2+1

dimensions

U(N)

gauge symmetry with

N > 1

for a quantum phase transition between an integer quantum Hall state and an insulator. We use modular transformations to generate from this theory new effective descriptions for quantum phase transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have abelian statistics. In the 't Hooft large

N

limit, the correlation length and dynamical critical exponents are independent of the particular transition in the absence of disorder. We argue that this conclusion survives away from the large

N

limit using recent duality conjectures and, thereby, provide theoretical support for the phenomenon of superuniversality found at distinct quantum Hall critical points.