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

Abstract

We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $\nu =1/m$(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 non-commutative 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.

11 pages, no figure,published version

References in corpus (6)

• Geometrical Description of the Fractional Quantum Hall Effect
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Model anisotropic quantum Hall states
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Quantum Hall effects in fast rotating Fermi gases with anisotropic dipolar interaction

Cited by in corpus (8)

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• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses