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Entanglement in Finitely Correlated Spin States

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Spyridon Michalakis, Bruno Nachtergaele

Mathematical Physics · Submitted 5 Jun 2006

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

The authors' main claim Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient .

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arXiv IDmath-ph/0606018 (version 3)
Pith IDSR2DLJYM, Pith's permanent record of this paper and its review
CitationBruno Nachtergaele, Spyridon Michalakis. "Entanglement in Finitely Correlated Spin States." arXiv:math-ph/0606018 (2006). https://pith.science/paper/SR2DLJYM
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,067 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.55 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. Finitely correlated states are otherwise known as matrix product states or generalized valence-bond states. The bounds become exact in the limit of the entanglement of a single spin and the half-infinite chain to the right (or the left) of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient . Our result also generalizes the study of entanglement in the ground state of the AKLT model by Fan, Korepin, and Roychowdhury. Our result permits one to calculate more efficiently, numerically and in some cases even analytically, the entanglement of arbitrary finitely correlated quantum spin chains.

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 derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. contribution 0.79 0.97 0.46 asserted 1.00
s1 Finitely correlated states are otherwise known as matrix product states or generalized valence-bond states. background 1.00 0.05 0.02 asserted 1.00
s2 The bounds become exact in the limit of the entanglement of a single spin and the half-infinite chain to the right (or the left) of it. result 0.93 0.82 0.14 asserted 1.00
s3 Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient . result 0.68 0.91 0.40 asserted 1.00
s4 Our result also generalizes the study of entanglement in the ground state of the AKLT model by Fan, Korepin, and Roychowdhury. contribution 0.59 0.73 0.06 asserted 1.00
s5 Our result permits one to calculate more efficiently, numerically and in some cases even analytically, the entanglement of arbitrary finitely correlated quantum spin chains. interpretation 0.84 0.86 0.14 asserted 0.67

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

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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 derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. Finitely correlated states are otherwise known as matrix product states or generalized valence-bond states. The bounds become exact in the limit of the entanglement of a single spin and the half-infinite chain to the right (or the left) of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient . Our result also generalizes the study of entanglement in the ground state of the AKLT model by Fan, Korepin, and Roychowdhury. Our result permits one to calculate more efficiently, numerically and in some cases even analytically, the entanglement of arbitrary finitely correlated quantum spin chains.

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