A new critical-amplitude relation which holds for one-dimensional quantum ground-state transitions is presented. The relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter. With the use of this relation, the exponent eta can be explicitly determined from only the scaling fit of the off-critical energy gap. The relation is confirmed in the transverse Ising model, the S= 1/2 anisotropic XY model, and the three-state Potts model.
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Hatano et al. (1994) studied this question.
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