Quantum criticality in dimerised anisotropic spin-1 chains

Abstract

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 $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.