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We calculate exactly cumulant generating functions (full counting statistics)for the transverse, staggered magnetization and the domain walls at zerotemperature for a finite interval of the XY spin chain. In particular, we alsoderive a universal interpolation formula in the scaling limit for the fullcounting statistics of the transverse magnetization and the domain walls whichis based on the solution of a Painlev\'e V equation. By further determiningsubleading corrections in a large interval asymptotics, we are able to test theapplicability of conformal field theory predictions at criticality. As abyproduct, we also obtain exact results for the probability of formation offerromagnetic and antiferromagnetic domains in both $\sigma^z$ and $\sigma^x$basis in the ground state. The analysis hinges upon asymptotic expansions ofblock Toeplitz determinants, for which we formulate and check numerically a newconjecture.

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