### 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 |
---|---|

Pages (from-to) | 21-26 |

Number of pages | 6 |

Journal | Physics Letters A |

Volume | 312 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jun 2 2003 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

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

**Asymptotic behavior of the emptiness formation probability in the critical phase of XXZ spin chain.** / Korepin, V. E.; Lukyanov, S.; Nishiyama, Yoshihiro; Shiroishi, M.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 312, no. 1-2, pp. 21-26. https://doi.org/10.1016/S0375-9601(03)00616-9

}

TY - JOUR

T1 - Asymptotic behavior of the emptiness formation probability in the critical phase of XXZ spin chain

AU - Korepin, V. E.

AU - Lukyanov, S.

AU - Nishiyama, Yoshihiro

AU - Shiroishi, M.

PY - 2003/6/2

Y1 - 2003/6/2

N2 - 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.

AB - 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.

KW - Asymptotic behaviours

KW - Correlation functions

KW - Density matrix renormalization

KW - Quantum spin chains

UR - http://www.scopus.com/inward/record.url?scp=0038413660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038413660&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(03)00616-9

DO - 10.1016/S0375-9601(03)00616-9

M3 - Article

AN - SCOPUS:0038413660

VL - 312

SP - 21

EP - 26

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1-2

ER -