Quantum criticality in dimerised anisotropic spin-1 chains

Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 $XXZ$ chain with single-ion anisotropy $D$. We demonstrate that the Haldane phase between large-$D$ and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-$D$ and antiferromagnetic phases with central charge $c=1\mathrm{/}2$, which terminates at a critical end-point where $c=7\mathrm{/}10$. Calculating the critical exponents of the order parameter, neutral gap and spin-spin-correlation function, we find $\beta =1\mathrm{/}8$ (1/24), $\nu =1$ (5/9), and $\eta =1\mathrm{/}4$ (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.