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This research establishes a rigorous mathematical link between multipartite entanglement in gapped quantum phases and topological quantum field theories (TQFTs), specifically verifying the conjecture for Levin-Wen string-net models. By demonstrating that ground state wavefunctions can determine modular tensor categories, this work advances our fundamental understanding of how complex quantum correlations encode low-energy physics descriptions. Such theoretical breakthroughs are essential for developing fault-tolerant topological qubits and scaling up practical quantum computing architectures.

Surse care acoperăarXiv, Quantum Computing Report, Quantum Zeitgeist

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From Multipartite Entanglement to TQFT

arXiv24 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2602.16770v2 Announce Type: replace-cross Abstract: At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional manifold $M$ -- in the ground state of a $(d-1)+1$-dimensional gapped theory and the partition function of the low energy TQFT on $M$. Under certain assumptions, the conjecture implies that for $d=3$, the ground state wavefunction can determine the modular tensor category description of the low energy TQFT. We verify our conjecture for general (2+1)-dimensional Levin-Wen string-net models.

Abstract:At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional manifold $M$ -- in the ground state of a $(d-1)+1$-dimensional gapped theory and the partition function of the low energy TQFT on $M$. Under certain assumptions, the conjecture implies that for $d=3$, the ground state wavefunction can determine the modular tensor category description of the low energy TQFT. We verify our conjecture for general (2+1)-dimensional Levin-Wen string-net models.

46 pages, 18 figures. v2: corrections (including the formula in the main conjecture), clarifications, additions

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Algebra (math.QA); Quantum Physics (quant-ph)

arXiv:2602.16770 [hep-th]

(or arXiv:2602.16770v2 [hep-th] for this version)

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