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We study an asymptotic behavior of a special correlator known as theEmptiness Formation Probability (EFP) for the one-dimensional anisotropic XYspin-1/2 chain in a transverse magnetic field. This correlator is essentiallythe probability of formation of a ferromagnetic string of length $n$ in theantiferromagnetic ground state of the chain and plays an important role in thetheory of integrable models. For the XY Spin Chain, the correlator can beexpressed as the determinant of a Toeplitz matrix and its asymptoticalbehaviors for $n \to \infty$ throughout the phase diagram are obtained usingknown theorems and conjectures on Toeplitz determinants. We find that the decayis exponential everywhere in the phase diagram of the XY model except on thecritical lines, i.e. where the spectrum is gapless. In these cases, a power-lawprefactor with a universal exponent arises in addition to an exponential orGaussian decay. The latter Gaussian behavior holds on the critical linecorresponding to the isotropic XY model, while at the critical value of themagnetic field the EFP decays exponentially. At small anisotropy one has acrossover from the Gaussian to the exponential behavior. We study thiscrossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due  to arxiv space limitations. If You would like to see the pdf with good  quality figures, please contact Fabio Franchini at  "fabio.franchini@stonybrook.edu

Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain