AbstractApplying 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.
Order parameter for the multichannel Kondo model at quantum criticality