  We study a correlation function for the one-dimensional isotropic ${XY}$
model (${XX0}$ model), which is called the Emptiness Formation Probability
(EFP). It is the probability of the formation of a ferromagnetic string in the
anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz
determinant, we discuss its asymptotic behaviors. We also compare the
analytical results with numerical calculations as the density-matrix
renormalization group and the quantum Monte-Carlo method.
