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Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
Strongly Correlated Electrons · Submitted 27 Feb 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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). | contribution 0.93 | 0.83 | 0.03 | asserted 0.97 |
| s1 | This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. | background 1.00 | 0.03 | 0.01 | asserted 1.00 |
| s2 | 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. | background 0.99 | 0.05 | 0.02 | asserted 0.79 |
| s3 | 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. | contribution 0.77 | 0.36 | 0.03 | unclear 0.65 |
| s4 | 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). | contribution 0.75 | 0.94 | 0.04 | asserted 0.90 |
| s5 | 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. | result 1.00 | 0.96 | 0.29 | asserted 1.00 |
| s6 | 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. | interpretation 1.00 | 0.65 | 0.95 | asserted 1.00 |
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The paper
Original 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.
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How the literature uses it
3 arXiv papers cite this in 15 sentences
Papers citing it · 9 sentences without a confident label
Builds on it 1 paper
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We have extended the Hall viscosity calculation of Ref. [ref] to the quantum Hall matrix model for the Blok-Wen series of non-Abelian fractional quantum Hall states [ref] .
Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model · Conclusion · 1.00
Uses its method or tool 1 paper
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To handle this divergent term we take the same approach as in [ref] and use the regularization procedure of Park and Haldane [ref] .
Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model · Hall viscosity in the matrix model · 0.98
Cites it as background 2 papers
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While the Hall viscosity can be computed retaining only long-wavelength features of the (gapped) quantum Hall state using its relationship to the Wen-Zee shift [ref] , and it has even been explored in the matrix model representation of non-commutative Chern-Simons theory [ref] , a microscopic derivation of the coupling of of the quantum Hall system to geometry has been lacking.
Lowest Landau level theory of the bosonic Jain states · Comments on geometric aspects · 0.88
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For two-dimensional quantum fluids, an anisotropic generalization of odd viscosity has recently been proposed in Refs. [ref] .
Anisotropic odd viscosity via time-modulated drive · Anisotropic odd viscosity · 0.81
What it cites · 4 sentences without a confident label
Cites as background 1 paper
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This metric parametrizes an anisotropy or intrinsic geometry of a FQH state, as discussed in the works of Haldane and collaborators [ref] .
"Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids · Hall viscosity in the presence of anisotropy · 0.82
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