Quantum spin chains from Onsager algebras and reflection $K$-matrices

Abstract

We present a representation of the generalized $p$-Onsager algebras $O_p(A_{n-1}^{(1)})$, $O_p(D_{n+1}^{(2)})$, $O_p(B_n^{(1)})$, $O_p({\tilde{B}}_n^{(1)})$ and $O_p(D_n^{(1)})$ in which the generators are expressed as local Hamiltonians of XXZ type spin chains with various boundary terms reflecting the Dynkin diagrams. Their symmetry is described by the reflection $K$ matrices which are obtained recently by a $q$-boson matrix product construction related to the 3D integrability and characterized by Onsager coideals of quantum affine algebras. The spectral decomposition of the $K$ matrices with respect to the classical part of the Onsager algebra is described conjecturally. We also include a proof of a certain invariance property of boundary vectors in the $q$-boson Fock space playing a key role in the matrix product construction.

arXiv comment24 pages, minor modifications

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Cited by in corpus (4)

• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Generalised Onsager Algebra in Quantum Lattice Models
• Integrable boundaries for the q-Hahn process
• Defining relations for quantum symmetric pair coideals of Kac-Moody type