Isotropic to anisotropic transition in a fractional quantum Hall state
Name
Mulligan-2010-Isotropic to anisotr.pdf
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Author(s)
Mulligan, Michael
Nayak, Chetan
Kachru, Shamit
Date Issued
August 2010
Journal
Physical Review B
Publisher
American Physical Society
Citation
Mulligan, Michael, Chetan Nayak, and Shamit Kachru. “Isotropic to anisotropic transition in a fractional quantum Hall state.” Physical Review B 82.8 (2010): 085102. © 2010 The American Physical Society.
Version
Final published version
Abstract
We study an Abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field ei2, characteristic of a quantum critical point with dynamical critical exponent z=2, and a level-k Chern-Simons coupling, which is marginal at this critical point. For k=0, this theory is dual to a free z=2 scalar field theory describing a quantum Lifshitz transition, but k≠0 renders the scalar description nonlocal. The k≠0 theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary and a nontrivial ground-state degeneracy kg when it is placed on a finite-size Riemann surface of genus g. The coefficient of ei2 is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. We compute zero-temperature transport coefficients in both phases and at the critical point and comment briefly on the relevance of our results to recent experiments.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.82.085102
