Continuous phase transition between Néel and valence bond solid phases in a J-Q -like spin ladder system

We investigate a quantum phase transition between a Néel 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-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 Néel-VBS transition is continuous and belongs to the Gaussian universality class with the central charge c=1. In particular, the critical exponents β,η, and, ν 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.