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Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction

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arxiv 2411.02162 v1 pith:6O4FEXT5 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 systemsintegrableclassconservedinteractionknownlocalnearest-neighbor
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General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial local conserved quantities. This result confirms that there are no missing integrable systems, i.e., integrable systems in this class are exactly those that are already known. In addition, this result excludes the possibility of intermediate systems which have a finite number of nontrivial local conserved quantities. Our findings support the expectation that integrable systems are exceptional in quantum many-body systems and most systems are non-integrable.

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Cited by 3 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.

  3. A Complexity-Based Approach to Quantum Observable Equilibration

    quant-ph 2025-06 conditional novelty 6.0 of 10

    The new Observable Equilibration Complexity Measure, entropy times L1 distance to the dephased equilibrium distribution, tracks equilibration and separates high- from low-effective-dimension dynamics.

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