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Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems

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O. Viyuela, A. Rivas, M.A. Martin-Delgado

Quantum Physics · Submitted 4 Sep 2013

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

The authors' main claim We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero.

how it is stated · asserted 1.00 read the record →

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arXiv ID1309.1174 (version 2)
Pith ID4Y4NWO3B, Pith's permanent record of this paper and its review
CitationA. Rivas, M.A. Martin-Delgado, O. Viyuela. "Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems." arXiv:1309.1174 (2013). https://pith.science/paper/4Y4NWO3B
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,254 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in 1D fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.

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 introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in 1D fermion systems, such as topological insulators and superconductors. contribution 1.00 0.89 0.14 asserted 1.00
s1 Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. contribution 0.36 0.13 0.06 asserted 0.92
s2 We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero. result 1.00 0.96 0.56 asserted 1.00
s3 This stands as a borderline between two different topological phases as a function of the temperature. interpretation 0.97 0.70 0.20 asserted 1.00
s4 Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems. result 0.74 0.82 0.09 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from simulation or computation 0.59.

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

We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in 1D fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.

Human review

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References
How later papers used it

61 later papers cite it

Evidence: substantial. 60 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 103 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Compares with it 1 of 7 papers with this label

  • Showed in its figure that in the limit g→0 its temperature gap of the Uhlmann phase tends to the known result for spin-1/2 fermions in crystal momentum k-space given by this paper.

    Thermal Uhlmann phase in a locally driven two-spin system (2023) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

3 arXiv papers cite this in 5 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper
  • In contrast to a previous finding that topological properties may not survive above a certain critical temperature, we find that topological properties of open systems, in the sense of the measure suggested here, can persist at any finite temperature and disappear only in the mathematical limit of infinite temperature.

    Topological characterization of one-dimensional open fermionic systems · 0.89

Papers citing it · 3 sentences without a confident label

Builds on it 1 paper
Compares with it 1 paper

What it cites

Cites as background 1 paper
  • In addition, the role played by external dissipative effects and thermal baths in topological insulators and superconductors has attracted much interest both in quantum simulations with different platforms and in condensed matter [ref] .

    Topology by dissipation · Introduction · 0.88

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