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Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction

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arxiv 2411.02163 v1 pith:P5D3CBSP submitted 2024-11-04 cond-mat.stat-mech math-phmath.MPquant-ph

Mizuki Yamaguchi , Yuuya Chiba , Naoto Shiraishi This is my paper · ORCID
classification cond-mat.stat-mechmath-phmath.MPquant-ph
keywords conservedquantitieslocalsystemsabsencechainsintegrableinteraction
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We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. This result shows that there are no further integrable system that awaits to be discovered. Our finding also implies that there is no intermediate systems with a finite number of nontrivial local conserved quantities. In addition, we clarify all short-support conserved quantities in non-integrable systems, which we need to take into account in analyses of thermalization and level statistics.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Simple Necessary and Sufficient Condition for Yang--Baxter Integrability

    cond-mat.stat-mech 2026-07 conditional novelty 8.0 of 10

    The Reshetikhin condition on a nearest-neighbour spin-chain Hamiltonian is sufficient (and necessary) for the existence of a regular difference-form Yang–Baxter R-matrix, resolving a 1980s conjecture.

  2. Rigorous Test for Quantum Integrability and Nonintegrability

    cond-mat.stat-mech 2025-01 conditional novelty 8.0 of 10

    A quantum spin chain with finite-range interactions is nonintegrable if no 3-local operator almost commutes with the Hamiltonian, a condition that can be checked by a system-size-independent algorithm.

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