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Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO($n$)

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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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Niklas Johansson, Erik Sjöqvist

Quantum Physics · Submitted 15 Jun 2004

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

The authors' main claim Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.

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arXiv IDquant-ph/0406105 (version 3)
Pith IDT33QFK3D, Pith's permanent record of this paper and its review
CitationErik Sj\"oqvist, Niklas Johansson. "Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO($n$)." arXiv:quant-ph/0406105 (2004). https://pith.science/paper/T33QFK3D
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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, 5,613 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.

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 Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. background 1.00 0.02 0.02 asserted 1.00
s1 Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. contribution 0.86 0.58 0.06 asserted 0.79
s2 This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. background 0.87 0.07 0.04 asserted 1.00
s3 We develop necessary means to determine the homotopy class of a given loop in this space. contribution 0.63 0.94 0.08 asserted 1.00
s4 Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. gap 0.55 0.28 0.03 hedged possibility 1.00
s5 To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. contribution 0.97 0.94 0.20 asserted 1.00
s6 Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information. result 0.99 0.89 0.26 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.83 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.

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