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

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

2002-10-07

arxiv.org/abs/cond-mat/0210140v2

Phys.Lett.A312:21-26,2003

Physics

Condensed Matter

Statistical Mechanics

9 pages, 2 figures

Scientific paper

10.1016/S0375-9601(03)00616-9

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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