Modified algebraic Bethe ansatz: twisted XXX case

DOI10.3842/SIGMA.2018.054zbMath1392.82020arXiv1804.00597OpenAlexW2796286839MaRDI QIDQ1639741

Samuel Belliard, Benoit Vallet, Nikita A. Slavnov

Publication date: 13 June 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.00597

zbMATH Keywords

algebraic Bethe ansatzintegrable spin chainBaxter T-Q equationquantum Wronskian equation

Mathematics Subject Classification ID

Renormalization group methods in equilibrium statistical mechanics (82B28) 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) Yang-Baxter equations (16T25)

Related Items

Analytical results on the Heisenberg spin chain in a magnetic field, Exact solution of the Heisenberg XX model with twisted boundary conditions, Wronskian-type formula for inhomogeneous \(TQ\) equations, Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame, Scalar product of twisted XXX modified Bethe vectors, Why scalar products in the algebraic Bethe ansatz have determinant representation, New compact construction of eigenstates for supersymmetric spin chains, Overlap between usual and modified Bethe vectors, Scalar products in twisted XXX spin chain. Determinant representation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bethe states of the XXZ spin-\(\frac{1}{2}\) chain with arbitrary boundary fields
• The \(R\)-matrix factorization, \(Q\)-operator, and variable separation in the case of the XXX spin chain with the \(SL(2,\mathbb C)\) symmetry group
• Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model
• 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
• Slavnov and Gaudin-Korepin formulas for models without \({\mathrm U}(1)\) symmetry: the twisted XXX chain
• Quantum inverse problem method. I
• Integrable SU(N) vertex models with general toroidal boundary conditions
• A note on \(\mathfrak{g}{\mathfrak{l}}_2 \)-invariant Bethe vectors
• Algebraic Bethe ansatz for the XXZ Gaudin models with generic boundary
• New construction of eigenstates and separation of variables for SU(\(N\)) quantum spin chains
• Algebraic geometry and Bethe ansatz. I: The quotient ring for BAE
• Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
• Heisenberg XXX model with general boundaries: eigenvectors from algebraic Bethe ansatz
• An inhomogeneousT-Qequation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• An inhomogeneous Lax representation for the Hirota equation
• Bethe vectors ofGL(3)-invariant integrable models
• Bethe equations `on the wrong side of the equator'
• Boundary conditions for integrable quantum systems
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• The scattering matrix for a generalgl(2) spin chain
• Off-Diagonal Bethe Ansatz for Exactly Solvable Models
• Fast analytic solver of rational Bethe equations
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Modified algebraic Bethe ansatz for XXZ chain on the segment. III. Proof