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Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain

V. E. Korepin·S. Lukyanov·Y. Nishiyama·M. Shiroishi
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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 P(n) ~ n^{-gamma} C^{-n^2}. 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 formulas, we employed an 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 formulas fairly definitely.

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V. E. Korepin, S. Lukyanov, Y. Nishiyama, M. Shiroishi. 2002-10-11. Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain. https://doi.org/10.1016/s0375-9601(03)00616-9

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