We investigate a quantum phase transition between a N\'eel phase and a valence bond solid (VBS) phase, each of which breaks a different
Z2 symmetry, in a spin-
1/2 two-leg XXZ ladder with a four-spin interaction. The model can be viewed as a one-dimensional variant of the celebrated $J\text{\ensuremath{-}}Q$ model on a square lattice. By means of variational uniform matrix product state calculations and an effective field theory, we determine the phase diagram of the model and present evidence that the N\'eel-VBS transition is continuous and belongs to the Gaussian universality class with the central charge
c=1. In particular, the critical exponents $\ensuremath{\beta},\ensuremath{\eta},$ and, $\ensuremath{\nu}$ are found to satisfy the constraints expected for a Gaussian transition within numerical accuracy. These exponents do not detectably change along the phase boundary while they are in general allowed to do so for the Gaussian class.
We study the transition between N\'eel and columnar valence-bond solid ordering in two-dimensional
S=3/2 square lattice quantum antiferromagnets with SO(3) symmetry. According to the deconfined criticality scenario, this transition can be direct and continuous like the well-studied
S=1/2 case. To study the global phase diagram, we work with four multi-spin couplings with full rotational symmetry, that are free of the sign-problem of quantum Monte Carlo. Exploring the phase diagram with quantum Monte Carlo simulations, we find that the phase transition between N\'eel and valence-bond solid is strongly first-order in the parts of the phase diagram that we have accessed.