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Measurement of Topological Order based on Metric-Curvature Correspondence

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Gero von Gersdorff, Wei Chen

Mesoscale and Nanoscale Physics · Submitted 28 Jun 2021

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

The authors' main claim We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space.

how it is stated · asserted 1.00 read the record →

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arXiv ID2106.14769 (version 2)
Pith ID4KXES5L6, Pith's permanent record of this paper and its review
CitationGero von Gersdorff, Wei Chen. "Measurement of Topological Order based on Metric-Curvature Correspondence." arXiv:2106.14769 (2021). https://pith.science/paper/4KXES5L6
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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, 3,063 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space. Based on this metric-curvature correspondence, a time-resolved and angle-resolved photoemission spectroscopy experiment is proposed to measure the violation of spectral sum rule caused by a pulse electric field to detect the quantum metric, from which the topological properties of the system may be extracted.

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 A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. background 1.00 0.06 0.07 asserted 1.00
s1 We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space. result 0.72 0.89 0.55 asserted 1.00
s2 Based on this metric-curvature correspondence, a time-resolved and angle-resolved photoemission spectroscopy experiment is proposed to measure the violation of spectral sum rule caused by a pulse electric field to detect the quantum metric, from which the topological properties of the system may be extracted. method 0.43 0.26 0.45 hedged possibility 0.84

What kind of paper the classifier reports this is: method or tool 0.52 · evidence from proof or derivation 0.65.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space. Based on this metric-curvature correspondence, a time-resolved and angle-resolved photoemission spectroscopy experiment is proposed to measure the violation of spectral sum rule caused by a pulse electric field to detect the quantum metric, from which the topological properties of the system may be extracted.

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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

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