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

• URL: http://arxiv.org/abs/2501.15506v2
• Date: Wed, 19 Mar 2025 12:23:22 GMT
• Title: Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Authors: Naoto Shiraishi,
• Abstract summary: We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction.<n>We classify the integrability and non-integrability of the above class of spin systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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