Emptiness Formation Probability and the Painleve` V equation

Abstract: The Emptiness Formation Probability is the probability of finding L consecutive down spins in the ground state of a spin 1/2 chain.
It represents perhaps the simplest correlator that can be calculated in a quantum spin chain. I will discuss this quantity in the XY spin chain, including the best-known example of the Ising spin chain in transverse field. It is shown, in particular,  that in the scaling limit, the Emptiness Formation Probability is the tau-function of a Painleve` V equation.
An explicit power series expansion of the tau-function is also provided. This is joint work with F. Ares (arXiv:1909.01270 ).