Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states

Abstract

We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model we compute the Hall viscosity, Hall conductance in a non-uniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states which are of current interest.

v2: 27 pages, 1 figure, minor typos corrected. To appear in PRB

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• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
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• Hall Viscosity of Composite Fermions
• Lowest Landau level theory of the bosonic Jain states
• Klein-Gordon theory in noncommutative phase space
• Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Composite anyons on a torus
• Anisotropic odd viscosity via time-modulated drive
• Higher bracket structure of density operators in Weyl fermion systems and topological insulators
• Bloch waves and Non-commutative Tori of Magnetic Translations