Emptiness Formation Probability for the Anisotropic XY Spin Chain in a Magnetic Field

TL;DR

This paper investigates the asymptotic decay of the Emptiness Formation Probability in the anisotropic XY spin chain under a magnetic field, revealing exponential decay with special behavior at critical lines.

Contribution

It provides a detailed analysis of EFP decay in the XY model, identifying exponential decay everywhere except at critical lines where it exhibits Gaussian decay or a power-law prefactor.

Findings

EFP decays exponentially in the XY model except at critical lines.

At the isotropic XY line, EFP decay is Gaussian.

At the critical magnetic field, EFP remains exponential with a universal power-law prefactor.

Abstract

We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length "n" in a ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n goes to 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 cond-mat/0106062. The other line is 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.