Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry

One dimensional (1d) interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel 1d physics was found numerically in systems with either spatially nonlocal interactions, or at the 1d boundary of 2d quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work found that the original (1+1)d boundary conformal field theory of a 2d SPT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the order-disorder quantum critical point, we find that by tuning one parameter at the boundary, there is a generic direct transition between the valence bond solid (VBS) order and another phase with potentially a long range Néel order. This transition is very similar to the Néel-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions.