Classification of reflection matrices related to (super) Yangians and application to open spin chain models

Abstract

We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz resolution for the so(m) and sp(n) open spin chains with boundary conditions described by the diagonal solutions.

36 pages ; references added ; typos corrected, precisions added

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• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
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• Bethe Ansatz equations and exact S matrices for the osp(M|2n) open super spin chain
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• On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system
• The Bethe Ansatz Equations for Reflecting Magnons
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Integrable boundary conditions for multi-species ASEP
• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• Gauge Theory and Boundary Integrability
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• New reflection matrices for the U_q(gl(m|n)) case
• On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• On the classification of rational K-matrices
• $OSp(n|2m)$ quantum chains with free boundaries
• Commuting quantum traces: the case of reflection algebras
• New boundary monodromy matrices for classical sigma models
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Reflection matrices for the $U_q[spo(2n|2m)]$ vertex model
• On sl(N) and sl(M|N) integrable open spin chains
• Fermionic reflection matrices
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model