Critical exponent in the magnetization curve of quantum spin chains

The ground-state magnetization curve around the critical magnetic field $H_c$ of quantum spin chains with a spin gap is investigated. We propose a size scaling method to estimate the critical exponent δ defined as $m\sim |H-H_c{|}^{1/\delta }$ from finite cluster calculation. The applications of the method to the $S=1\mathrm{}$ antiferromagnetic chain and $S=1/2\mathrm{}$ bond-alternating chain lead to a common conclusion that $\delta =2.\mathrm{}$ The same result is derived for both edges of the magnetization plateau of the $S=3/2\mathrm{}$ antiferromagnetic chain with single-ion anisotropy.