On the separation of variables for the modular XXZ magnet and the lattice sinh-Gordon models

DOI10.1007/s00023-019-00806-2zbMath1427.82004arXiv1806.04487OpenAlexW3101844482WikidataQ127865591 ScholiaQ127865591MaRDI QIDQ2001961

Karol Kajetan Kozlowski, Alexander N. Manashov, Sergey E. Derkachov

Publication date: 11 July 2019

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04487

zbMATH Keywords

latticesinh-Gordon modelGauss-Givental integral representationmodular XXZ magnet

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40)

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Cites Work

• Exact solution of the Faddeev-Volkov model
• Unitary representations of \(U_{q} (\mathfrak s\mathfrak l(2,\mathbb R))\), the modular double and the multiparticle \(q\)-deformed Toda chain
• R-operator, co-product and Haar-measure for the modular double of \(U_q(\mathfrak{sl}(2,\mathbb R))\).
• Baxter operators with deformed symmetry
• Unitarity of the SoV transform for the Toda chain
• Transition function for the Toda chain
• Faddeev-Volkov solution of the Yang-Baxter equation and discrete conformal symmetry
• Integral representations for the eigenfunctions of quantum open and periodic Toda chains from the QISM formalism
• Iterative construction of eigenfunctions of the monodromy matrix for $SL(2,\mathbb {C})$ magnet
• The eight-vertex model with quasi-periodic boundary conditions
• The Yang–Baxter relation and gauge invariance
• The sine–Gordon model revisited: I
• Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model
• The periodic Toda chain and a matrix generalization of the Bessel function recursion relations
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• Baxter Operator and Baxter Equation for q-Toda and Toda₂ Chains
• Baxter'sQ-operator for the homogeneousXXXspin chain
• The spectral theory of a functional-difference operator in conformal field theory
• The R-operator for a modular double
• Aspects of the inverse problem for the Toda chain
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables
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