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
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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 -