Classifying nearest-neighbour interactions and deformations of AdS

Abstract

We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbour interactions. We find a total of four independent solutions. Two are related to the usual six- and eight-vertex models that have R-matrices of difference form. We find two completely new solutions of the Yang-Baxter equation, which are manifestly of non-difference form. These new solutions contain the S-matrices of the AdS2 and AdS3 integrable models as a special case. Consequently, we can classify all possible integrable deformations of eight-vertex type of these holographic integrable systems.

arXiv comment6 pages

References in corpus (18)

• Review of AdS/CFT Integrability: An Overview
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Long-Range Deformations for Integrable Spin Chains
• Towards integrability for AdS3/CFT2
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Lectures on Yangian Symmetry
• Integrability Test for Spin Chains
• Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• Ladder operator for the one-dimensional Hubbard model
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• The S-matrix algebra of the AdS2 X S2 superstring
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• Integrable Deformations of the XXZ Spin Chain
• Integrability and duality in spin chains
• Something interacting and solvable in 1d

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• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• Boost generator in AdS_3 integrable superstrings for general braiding
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• A study of integrable form factors in massless relativistic AdS_3
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• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Integrability and charge transport in asymmetric quantum-circuit geometries
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• Flag Integrable Models and Generalized Graded Algebras
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