Continuous phase transition between Neel and valence bond solid phases on a spin ladder system

We investigate a quantum phase transition between a Neel phase and a valence bond solid (VBS) phase in the J-Q-like model in one spatial dimension.
We study a spin-1/2 two-leg XXZ ladder with a four-spin interaction with the use of the variational uniform matrix product state algorithm and an effective field theory.
We determine the phase diagram and present evidences that the Neel-VBS transition belongs to the Gaussian universality class.