Off-diagonal Bethe Ansatz on the $so(5)$ spin chain

Abstract

The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing to those in [1]) to determine the spectrum of the transfer matrices are derived. For the periodic case, we recover the results obtained in \cite{NYReshetikhin1}, while for the non-diagonal boundary case, a new inhomogeneous $T-Q$ relation is constructed. The present method can be directly generalized to deal with the $so(2n+1)$ (i.e., $B_n$) quantum integrable spin chains with general boundaries.

arXiv commentPublished version, 42 pages, no figure

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• Exact solutions of the $C_n$ quantum spin chain
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model
• T-W relation and free energy of the Heisenberg chain at a finite temperature
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Exact solution of the $q$-deformed $D_3^{(1)}$ vertex model with open boundaries
• Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries