Correlation functions by separation of variables: the XXX spin chain

We explain how to compute correlation functions at zero temperature within the framework of quantum version Separation Variables (SoV) in case a simple model: XXX Heisenberg chain spin 1/2 with twisted (quasi-periodic) boundary conditions. first detail all steps our method anti-periodic The model can be solved SoV by introducing inhomogeneity parameters. action local operators on eigenstates are then naturally expressed terms multiple sums over these transform parameters into contour integrals. Evaluating integrals residues poles outside integration contours, we rewrite this as sum involving roots Baxter polynomial plus contribution infinity. show that infinity vanishes thermodynamic limit, and recover limit for zero-temperature integral representation had been previously obtained through study periodic Bethe Ansatz or infinite volume q-vertex operator approach. finally easily generalized more general non-diagonal twist: corresponding weights different finite modified, but same than case, hence proving independence respect particular form twist.