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, Y.

AU - Shiroishi, M.

N1 - Funding Information:
We thank A. Abanov, H. Boos, F. Essler, F. Smirnov, M. Takahashi and A. Zamolodchikov for useful discussions. V. Korepin was supported by NSF Grant PHY-9988566, S. Lukyanov was supported in part by DOE Grant DE-FG02-96ER40959, Y. Nishiyama was supported by Grant-in-Aid for Young Scientists No. 13740240, M. Shiroishi was supported by Grant-in-Aid for Young Scientists No. 14740228.

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

SN - 0375-9601

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

IS - 1-2

ER -