Short distance correlators in the XXZ spin chain for arbitrary string distributions

In this paper, we consider expectation values of local correlators in highly excited states of the spin-1/2 XXZ chain. Assuming that the string hypothesis holds we formulate the following conjecture: The correlation functions can be computed using the known factorized formulae of the finite temperature situation, if the building blocks are computed via certain linear integral equations using the string densities only. We prove this statement for the nearest neighbour z-z correlator for states with arbitrary string densities. Also, we check the conjecture numerically for other correlators in the finite temperature case. Our results pave the way towards the computation of the stationary values of correlators in non-equilibrium situations using the quench action approach.