### 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^{-γ} C^{-n2}. Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent γ. 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.

Original language | English |
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Pages (from-to) | 21-26 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 312 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jun 2 2003 |

### Keywords

- Asymptotic behaviours
- Correlation functions
- Density matrix renormalization
- Quantum spin chains

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*312*(1-2), 21-26. https://doi.org/10.1016/S0375-9601(03)00616-9