02-415 V. E. Korepin, S. Lukyanov, Y. Nishiyama, M. Shiroishi

Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain (197K, Postscript) Oct 7, 02

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Abstract. We study the Emptiness Formation Probability (EFP) for the spin 1/2 $XXZ$ spin chain. EFP $P(n)$ detects a formation of ferromagnetic string of the length $n$ in the ground state. It is expected that EFP decays in a Gaussian way for large strings Here, we propose the explicit expressions for the rate of Gaussian decay ${C}$ as well as for the exponent $\gamma$.In order to confirm the validity of our formulae, we employed an {\it ab initio} simulation technique of the density-matrix renormalization group to simulate $XXZ$ spin chain of sufficient length. Furthermore, we performed Monte-Carlo integration of the Jimbo-Miwa multiple integral for ${P(n)}$. Those numerical results for ${P(n)}$ support our formulae fairly definitely.

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