Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

Abstract

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A_n^{(1)}$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.

4 pages, plain tex, UMTG-167

Cited by in corpus (99)

• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• XXZ chain with a boundary
• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Integrable XYZ Spin Chain with Boundaries
• Correlation functions of the open XXZ chain I
• Deriving Boundary S Matrices
• Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Correlation functions of the open XXZ chain II
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Integrable open-boundary conditions for the $q$-deformed supersymmetric $U$ model of strongly correlated electrons
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and open spin chains in any representation
• Reflection K-Matrices for 19-Vertex Models
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
• Analytical Bethe Ansatz for $A_{2n-1}^{(2)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ quantum-algebra-invariant open spin chains
• Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
• R-matrices and Spectrum of Vertex Models based on Superalgebras
• Boundary quantum group generators of type A
• Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg Chain
• From affine Hecke algebras to boundary symmetries
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries
• Low-Temperature Thermodynamics of $A_2^{(2)}$ and su(3)-invariant Spin Chains
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Bethe Ansatz solution for quantum spin-1 chains with boundary terms
• Integrability of the $D_n^2$ vertex models with open boundary
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• $C_n^{(1)}$, $D_n^{(1)}$ and $A_{2n-1}^{(2)}$ reflection K-matrices
• Integrable Chain Model with Additional Staggered Model Parameter
• Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
• Introduction to Quantum Integrability
• Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions
• The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model
• Reflection $K$-matrices related to Temperley-Lieb $R$-matrices
• Algebraic Bethe Ansatz for the Zamolodchikov-Fateev and Izergin-Korepin models with open boundary conditions
• A quantum algebraic description of D-branes on group manifolds
• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries
• Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance
• Integrable O(n) model on the honeycomb lattice via reflection matrices : Surface critical behaviour
• An Ising model in a magnetic field with a boundary
• Exact solution for the Bariev model with boundary fields
• Surveying the quantum group symmetries of integrable open spin chains
• B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices
• Trigonometric sl(2) Gaudin model with boundary terms
• The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
• Diagonal $K$-matrices and transfer matrix eigenspectra associated with the $G_2^{(1)}$ $R$-matrix
• On Separation of Variables for Reflection Algebras
• Nonstandard coproducts and the Izergin-Korepin open spin chain
• Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models
• Integrable supersymmetric correlated electron chain with open boundaries
• Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary
• An open-boundary integrable model of three coupled XY spin chains
• Symmetry Algebras of Large-N Matrix Models for Open Strings
• D_{n+1}^(2) Reflection K-matrices
• New D_{n+1}^(2) K-matrices with quantum group symmetry
• Universal Bethe ansatz solution for the Temperley-Lieb spin chain
• A remark on ground state of boundary Izergin-Korepin model
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• A supersymmetric U_{q}[osp(2|2)]-extended Hubbard model with boundary fields
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• The spectrum of quantum-group-invariant transfer matrices
• Algebraic Bethe Ansatz solutions for the $sl(2|1{)}^{(2)}$ and $osp(2|1)$ models with boundary terms
• Thermodynamic properties of an integrable quantum spin ladder with boundary impurities
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains
• On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model
• Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• Asymmetric Twin Representation: the Transfer Matrix Symmetry
• Diagonal solutions to reflection equations in higher spin XXZ model
• Spin chains with boundary inhomogeneities
• Integrable open boundary conditions for the Bariev model of three coupled XY spin chains
• Reflection matrices for the $U_q[spo(2n|2m)]$ vertex model
• Reflection $K$-matrices for a nineteen vertex model with $U_q[\mathrm{osp}{\left(2|2\right)}^{\left(2\right)}]$ symmetry
• Field theoretic models on covariant quantum spaces
• Brane Bulk Couplings and Condensation from REA Fusion
• Classically and Quantum Integrable Systems with Boundary
• Exact surface energy of the Hubbard model with nonparallel boundary magnetic fields
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries