Emptiness Formation Probability for the One-Dimensional Isotropic XY Model

Abstract

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.

20 pages, 7 figures, to be published in J. Phys. Soc. Jpn

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