Algebraic Bethe ansatz for the open XXZ spin chain with non-diagonal boundary terms via \(U_{\mathfrak{q}}\mathfrak{sl}_2\) symmetry
DOI10.3842/sigma.2023.046zbMath1530.81105arXiv2212.09696OpenAlexW4384448116MaRDI QIDQ6172016
Jesper Lykke Jacobsen, Hubert Saleur, Dmitry Chernyak, Azat M. Gainutdinov
Publication date: 16 August 2023
Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.09696
Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Symmetry breaking in quantum theory (81R40) Exactly solvable models; Bethe ansatz (82B23) Exactly and quasi-solvable systems arising in quantum theory (81U15) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Yang-Baxter equations (16T25) Fusion categories, modular tensor categories, modular functors (18M20) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)
Cites Work
- Unnamed Item
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- Spaces of quasi-exponentials and representations of the Yangian \(Y(\mathfrak{gl}_N)\)
- Spin chains with non-diagonal boundaries and trigonometric SOS model with reflecting end
- Conformal boundary conditions in the critical \({\mathcal O}(n)\) model and dilute loop models
- Conformal boundary loop models
- Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum
- Modified algebraic Bethe ansatz for XXZ chain on the segment - I: Triangular cases
- Modified algebraic Bethe ansatz for XXZ chain on the segment. II: General cases
- Conformal two-boundary loop model on the annulus
- The two-boundary Temperley-Lieb algebra.
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
- Quantum affine algebras
- The blob algebra and the periodic Temperley-Lieb algebra
- The Temperley-Lieb algebra at roots of unity
- Exact solution of XXZ spin chain with unparallel boundary fields
- Functional relations and Bethe Ansatz for the \(XXZ\) chain
- Reflection \(K\)-matrices of the 19-vertex model and \(XXZ\) spin-1 chain with general boundary terms
- Baxterisation of the fused Hecke algebra and \(R\)-matrices with \(gl(N)\)-symmetry
- Completeness of Wronskian Bethe equations for rational \(\mathfrak{gl}_{\mathsf{m}|\mathsf{n}}\) spin chains
- On generalized \(Q\)-systems
- On zero-remainder conditions in the Bethe ansatz
- Integrability of Liouville theory: proof of the DOZZ formula
- Boundary matrices for the higher spin six vertex model
- Heisenberg XXX model with general boundaries: eigenvectors from algebraic Bethe ansatz
- Solution of the \(\text{SU}(N)\) vertex model with non-diagonal open boundaries
- Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
- \(U_{\mathfrak{q}}\mathfrak{sl}_2 \)-invariant non-compact boundary conditions for the XXZ spin chain
- Equivalences between spin models induced by defects
- Exercises with the universalR-matrix
- Bethe ansatz for the Temperley–Lieb loop model with open boundaries
- Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries
- Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables
- ON SCHUR-WEYL DUALITY, An HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$
- ON COMMUTANTS, DUAL PAIRS AND NON-SEMISIMPLE ALGEBRAS FROM STATISTICAL MECHANICS
- Boundary K-matrices for the six vertex and the n(2n-1)An-1vertex models
- Solutions of the boundary Yang Baxter equation for arbitrary spin
- Hecke algebraic approach to the reflection equation for spin chains
- 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
- Boundary K-matrices for the XYZ, XXZ and XXX spin chains
- Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory
- Combinatorial aspects of boundary loop models
- Off-Diagonal Bethe Ansatz for Exactly Solvable Models
- Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
- Quantum groups
- Modified algebraic Bethe ansatz for XXZ chain on the segment. III. Proof
- BAXTERIZATION
