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arXiv · 2501.15506

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

Naoto Shiraishi
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Abstract

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.

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Naoto Shiraishi. 2025-01-26. Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction. https://doi.org/10.1007/s10955-025-03551-5

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