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We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$.In absence of an explicit dimerization there are three phases: a large-$D$, anantiferromagnetically ordered and a Haldane phase. This phase structurepersists up to a critical dimerization, above which the Haldane phasedisappears. We show that for weak dimerization the phases are separated byGaussian and Ising quantum phase transitions. One of the Ising transitionsterminates in a critical point in the universality class of the dilute Isingmodel. We comment on the relevance of our results to experiments onquasi-one-dimensional anisotropic spin-1 quantum magnets.

Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy