The open XXX spin chain in the SoV framework: scalar product of separate states

Understand

We consider the XXX open spin-1/2 chain with the most general non-diagonal boundary terms, that we solve by means of the quantum separation of variables (SoV) approach.

• We compute the scalar products of separate states, a class of states which notably contains all the eigenstates of the model.
• As usual for models solved by SoV, these scalar products can be expressed as some determinants with a non-trivial dependance in terms of the inhomogeneity parameters that have to be introduced for the method to be applicable.
• We show that these determinants can be transformed into alternative ones in which the homogeneous limit can easily be taken.