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 a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order and competing six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector K=(2π/3,-2π/3). We present quantum Monte Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.