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We calculate the spin gap of homogeneous and inhomogeneous spin chains, using the White's density matrix renormalization group technique. We found that the spin gap is related to the ration between the spin velocity and the correlation exponent. We consider a spin superlattice, which is composed of a repeated pattern of two spin-1/2 XXZ chains with different anisotropy parameters. The behavior of the charge velocity as a function of the anisotropy parameter and the relative size of sub-chains was investigated. We found reasonable agreement between the bosonization results and the numerical ones.

The effective charge velocity of spin-¹/2 superlattices