Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

DOI10.1088/1742-5468/2014/05/P05015zbMath1456.82057arXiv1401.4901OpenAlexW3102851696MaRDI QIDQ3301954

Jean-Michel Maillet, Giuliano Niccoli, N. A. Kitanine

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4901

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Quantum equilibrium statistical mechanics (general) (82B10)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Generalized coordinate Bethe ansatz for non-diagonal boundaries
• Completeness of Bethe ansatz by Sklyanin SOV for cyclic representations of integrable quantum models
• Spin chains with non-diagonal boundaries and trigonometric SOS model with reflecting end
• Reconstruction of Baxter \(\mathbf Q\)-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• The \(q\)-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach
• Quantum inverse problem method. I
• Separation of variables in the open \(XXX\) chain
• Factorizing particles on a half-line and root systems
• Poisson structure of a periodic classical XYZ-chain
• Exact solution of XXZ spin chain with unparallel boundary fields
• Form factors of the \(XXZ\) Heisenberg spin-\(\frac 12\) finite chain
• Correlation functions of the \(XXZ\) Heisenberg spin-\({1\over 2}\) chain in a magnetic field
• Poisson structure of classical XXZ-chain
• Antiperiodic spin-1/2 \(XXZ\) quantum chains by separation of variables: complete spectrum and form factors
• Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-\(\frac{1}{2}\) chains with arbitrary boundary fields
• Heisenberg XXX model with general boundaries: eigenvectors from algebraic Bethe ansatz
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the \(XXZ\) model with non-diagonal twisted and open boundary conditions
• Partition function of the eight-vertex lattice model
• An inhomogeneousT-Qequation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• Algebraic Bethe ansatz for the six vertex model with upper triangularK-matrices
• Functional Bethe ansatz methods for the openXXXchain
• Bethe ansatz for the Temperley–Lieb loop model with open boundaries
• The sine–Gordon model revisited: I
• On the form factors of local operators in the lattice sine–Gordon model
• Non-diagonal open spin-1/2XXZquantum chains by separation of variables: complete spectrum and matrix elements of some quasi-local operators
• The complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Boundary conditions for integrable quantum systems
• An antiperiodic dynamical six-vertex model: I. Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic eight-vertex model
• A deformed analogue of Onsager’s symmetry in the XXZ open spin chain
• One-boundary Temperley–Lieb algebras in the XXZ and loop models
• Bethe ansatz derived from the functional relations of the openXXZchain for new special cases
• Correlation functions of the openXXZchain: I
• Boundary energy of the open XXX chain with a non-diagonal boundary term
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• SOV approach for integrable quantum models associated with general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Correlation functions of the openXXZchain: II
• On the quantum inverse scattering problem.
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables
• Solving the open \(XXZ\) spin chain with nondiagonal boundary terms at roots of unity