Title: Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain

Abstract: We calculate exactly cumulant generating functions (full counting statistics) for the transverse, staggered magnetization and the domain walls at zero temperature for a finite interval of the XY spin chain. In particular, we also derive a universal interpolation formula in the scaling limit for the full counting statistics of the transverse magnetization and the domain walls which is based on the solution of a Painlev\'e V equation. By further determining subleading corrections in a large interval asymptotics, we are able to test the applicability of conformal field theory predictions at criticality. As a byproduct, we also obtain exact results for the probability of formation of ferromagnetic and antiferromagnetic domains in both $\sigma^z$ and $\sigma^x$ basis in the ground state. The analysis hinges upon asymptotic expansions of block Toeplitz determinants, for which we formulate and check numerically a new conjecture.