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Universal relation between the dispersion curve and the ground-state correlation length in 1D antiferromagnetic quantum spin systems

K. Okunishi·Y. Akutsu·N. Akutsu·T. Yamamoto
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Abstract

We discuss an universal relation $ε(iκ)=0$ with ${\rm Re} κ=1/ξ$ in 1D quantum spin systems with an excitation gap, where $ε(k)$ is the dispersion curve of the low-energy excitation and $ξ$ is the correlation length of the ground-state. We first discuss this relation for integrable models such as the Ising model in a transverse filed and the XYZ model. We secondly make a derivation of the relation for general cases, in connection with the equilibrium crystal shape in the corresponding 2D classical system. We finally verify the relation for the S=1 bilinear-biquadratic spin chain and $S=1/2$ zigzag spin ladder numerically.

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K. Okunishi, Y. Akutsu, N. Akutsu, T. Yamamoto. 2001-07-02. Universal relation between the dispersion curve and the ground-state correlation length in 1D antiferromagnetic quantum spin systems. https://doi.org/10.1103/physrevb.64.104432

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