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Rigidity of the Laughlin liquid

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Elliott Lieb, Nicolas Rougerie (LPMMC), Jakob Yngvason

Mathematical Physics · Submitted 13 Sep 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value.

how it is stated · asserted 1.00 read the record →

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arXiv ID1609.03818 (version 5)
Pith IDYANWUK32, Pith's permanent record of this paper and its review
CitationElliott Lieb, Jakob Yngvason, Nicolas Rougerie (LPMMC). "Rigidity of the Laughlin liquid." arXiv:1609.03818 (2016). https://pith.science/paper/YANWUK32
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,642 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.37 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.63 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor $1/\ell$ and an analytic function of the N variables. This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. Consequences of this bound for the response of the Laughlin state to external fields are discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor $1/\ell$ and an analytic function of the N variables. contribution 0.67 0.39 0.04 asserted 0.83
s1 This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. background 0.71 0.19 0.05 asserted 0.98
s2 We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. result 1.00 0.94 0.88 asserted 1.00
s3 Consequences of this bound for the response of the Laughlin state to external fields are discussed. interpretation 0.98 0.56 0.04 unclear 0.91

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v5
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor $1/\ell$ and an analytic function of the N variables. This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. Consequences of this bound for the response of the Laughlin state to external fields are discussed.

Human review

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How the literature uses it

5 arXiv papers cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 7 sentences without a confident label

Cites it as support 1 paper
Cites it as background 1 paper

What it cites · 7 sentences without a confident label

Uses the method or tool of 1 paper
Cites as background 1 paper
  • In theoretical studies of the fractional quantum Hall effect (FQHE) [ref] Laughlin's wave function(s) [ref] play a fundamental role.

    Quantum Hall Effects · The Laughlin phase · 1.00

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