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

We consider quantum quenches in the integrable -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 'soliton-non-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 -invariant Hamiltonians with open boundary conditions. (paper: quantum statistical physics, condensed matter, integrable systems)