Exact solution of the C2(1) quantum spin chain with open boundary condition

Abstract

In this paper, we studied the exact solution of the $C_2^{\left(1\right)}$ invariant quantum spin chain with off-diagonal open boundary condition. We obtain a solution of the reflection equation where the all matrix element of reflection matrix are nonzeros. By using the technique of fusion, we construct the fused transfer matrix and find the closed recursive relations among the transfer matrices. Based on the algebraic analysis, we obtain the eigenvalue of the system and express it as the inhomogeneous $T-Q$ relation.