Emptiness formation probability for the anisotropic XY spin chain in a magnetic field

We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length n in the ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n --> infinity. We find that it is exponential everywhere in the phase diagram of the XY model except at the critical lines where the spectrum is gapless. One of those lines corresponds to the isotropic XY model where EFP decays in a Gaussian way, as was shown in [J. Phys. Soc. Jpn. 70 (2001) 3535]. The other lines are at the critical value of the magnetic field. There, we show that EFP is still exponential but acquires a non-trivial power-law prefactor with a universal exponent. (C) 2003 Elsevier B.V. All rights reserved.