Integrability of the $D_n^2$ vertex models with open boundary

Abstract

We investigate various aspects of the integrability of the vertex models associated to the $D_n^2$ affine Lie algebra with open boundaries. We first study the solutions of the corresponding reflection equation compatible with the minimal symmetry of this system. We find three classes of general solutions, one diagonal solution and two non-diagonal families with a free parameter. Next we perform the Bethe ansatz analysis for some of the associated open $D_2^2$ spin chains and we identify the boundary having quantum group invariance. We also discuss a new $D_2^2$ $R$-matrix.

latex, 20 pages

References in corpus (2)

• Reflection K-Matrices for 19-Vertex Models
• Nonstandard coproducts and the Izergin-Korepin open spin chain

Cited by in corpus (24)

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• Surveying the quantum group symmetries of integrable open spin chains
• B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices
• The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
• Towards the solution of an integrable $D_2^{(2)}$ spin chain
• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• D_{n+1}^(2) Reflection K-matrices
• New D_{n+1}^(2) K-matrices with quantum group symmetry
• Integrable boundary conditions for staggered vertex models
• The spectrum of quantum-group-invariant transfer matrices
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• Thermodynamic properties of an integrable quantum spin ladder with boundary impurities
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Spectrum of the transfer matrices of the spin chains associated with the $A_3^{(2)}$ Lie algebra
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models