Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction

Fuente: arXiv
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Auteur principal: Shiraishi, Naoto
Format: Preprint
Publié: 2025
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author Shiraishi, Naoto
author_facet Shiraishi, Naoto
contents We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15506
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
Shiraishi, Naoto
Statistical Mechanics
Strongly Correlated Electrons
Mathematical Physics
Quantum Physics
We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities.
title Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
topic Statistical Mechanics
Strongly Correlated Electrons
Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2501.15506