\(R\)-matrix-valued Lax pairs and long-range spin chains

DOI10.1016/j.physletb.2018.03.062zbMath1398.81111arXiv1801.08908OpenAlexW2785028633MaRDI QIDQ1800732

I. Sechin, Andrei V. Zotov

Publication date: 24 October 2018

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.08908

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Special quantum systems, such as solvable systems (81Q80)

Related Items

Elliptic generalisation of integrable q-deformed anisotropic Haldane–Shastry long-range spin chain ⋮ Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities ⋮ Integrable system of generalized relativistic interacting tops ⋮ Trigonometric integrable tops from solutions of associative Yang-Baxter equation ⋮ On R-matrix valued Lax pairs for Calogero–Moser models ⋮ Generalized model of interacting integrable tops ⋮ Calogero-Moser model and \(R\)-matrix identities ⋮ Quadratic algebras based on \(SL(NM)\) elliptic quantum \(R\)-matrices ⋮ Multi-pole extension of the elliptic models of interacting integrable tops ⋮ Odd supersymmetrization of elliptic R-matrices ⋮ A slow review of the AGT correspondence

Cites Work

• Unnamed Item
• Trigonometric version of quantum-classical duality in integrable systems
• Higher-order analogues of the unitarity condition for quantum \(R\)-matrices
• The commutativity of integrals of motion for quantum spin chains and elliptic functions identities
• Classical Yang-Baxter equation and the \(A_\infty\)-constraint
• Quantum Baxter-Belavin \(R\)-matrices and multidimensional Lax pairs for Painlevé VI
• On the connection between the one-dimensional \(S=1/2\) Heisenberg chain and Haldane-Shastry model
• Some algebraic structures connected with the Yang-Baxter equation
• The finite Toda lattices
• Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
• Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations
• Monopoles, duality and chiral symmetry breaking in \(N=2\) supersymmetric QCD
• Dynamical symmetry of integrable quantum systems
• The Yang-Baxter equation, symmetric functions, and Schubert polynomials
• Partition function of the eight-vertex lattice model
• Integrability of Calogero-Moser Spin System