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Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level

Xi Luo1,*, Yong-Shi Wu2,3,4, and Yue Yu1,2,3

  • 1Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
  • 2Center for Field Theory and Particle Physics and State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China
  • 3Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China
  • 4Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA

  • *xiluo@itp.ac.cn
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Phys. Rev. D 93, 125005 – Published 6 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.125005

Abstract

We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in ν=1/m(m  odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological noncommutative Chern-Simons theory. Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional quantum Hall (FQH) states besides the filling factor, are naturally defined. A noncommutative K-matrix Chern-Simons theory is proposed as a generalization to a large class of Abelian FQH topological orders.

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Phys. Rev. D 93, 125005– Published 6 June, 2016
  • Received 31 August 2013

© 2016 American Physical Society

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