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

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