Integrable quenches in nested spin chains II: Fusion of boundary transfer matrices

We consider quantum quenches in the integrable SU(3)-invariant spin chain (Lai Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to solitonnon-preserving boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: This is achieved by deriving a set of functional relations between the eigenvalues of certain fused operators that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T-and Y-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of SU(3)-invariant Hamiltonians with open boundary conditions.