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Finite-size scaling for correlations of quantum spin chains at criticality

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Abstract

We study the finite-size scaling behavior of two-point correlation functions of translationally invariant many-body systems at criticality. We propose an efficient method for calculating the two-point correlation functions in the thermodynamic limit from numerical data of finite systems. Our method is most effective when applied to a two-dimensional (classical) system which possesses a conformal invariance. By using this method with numerical data obtained from exact diagonalizations and Monte Carlo simulations, we study the spin-spin correlations of the quantum spin-1/2 and-3/2 antifierromagnetic chains. In particular, the logarithmic corrections to power-law decay of the correlation of the spin-1/2 isotropic Heisenberg antiferromagnetic chain are studied thoroughly. We clarify the cause of the discrepancy in previous calculations for the logarithmic corrections. Our result strongly supports the field-theoretic prediction based on the mappings to the Wess-Zumino-Witten nonlinear σ-model or the sine-Gordon model. We also treat logarithmic corrections and crossover phenomena in the spin-spin correlation of the spin-3/2 isotropic Heisenberg antiferromagnetic chain. Our results are consistent with the Affleck-Haldane prediction that the correlation of the spin-3/2 chain exhibits a crossover to the same asymptotic behavior as in the spin-1/2 chain.

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  1. Nobuyuki Mizukoshi

    Present address: NEC ULSI Systems Development Laboratories, Shimonumabe, Nakaharaku, 211, Kawasaki-shi, Kanagawa, Japan

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  1. Department of Physics, Gakushuin University, Mejiro, Toshima-ku, 171, Tokyo, Japan

    Tohru Koma & Nobuyuki Mizukoshi

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  1. Tohru Koma
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Koma, T., Mizukoshi, N. Finite-size scaling for correlations of quantum spin chains at criticality. J Stat Phys 83, 661–726 (1996). https://doi.org/10.1007/BF02183744

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