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One dimensional (1d) interacting systems with local Hamiltonianscan be studied with various well-developed analytical methods.Recently novel 1d physics was found numerically in systems witheither spatially nonlocal interactions, or at the 1d boundary of2d quantum critical points, and the critical fluctuation in thebulk also yields effective nonlocal interactions at the boundary.This work studies the edge states at the 1d boundary of 2dstrongly interacting symmetry protected topological (SPT) states,when the bulk is driven to a disorder-order phase transition. Wewill take the 2d Affleck-Kennedy-Lieb-Tasaki (AKLT) state as anexample, which is a SPT state protected by the SO(3) spinsymmetry and spatial translation. We found that the original(1+1)d boundary conformal field theory of the AKLT state isunstable due to coupling to the boundary avatar of the bulkquantum critical fluctuations. When the bulk is fixed at thequantum critical point, within the accuracy of our expansionmethod, we find that by tuning one parameter at the boundary,there is a generic direct transition between the long rangeantiferromagnetic Néel order and the valence bond solid (VBS)order. This transition is very similar to the Néel-VBStransition recently found in numerical simulation of a spin-1/2chain with nonlocal spatial interactions. Connections between ouranalytical studies and recent numerical results concerning theedge states of the 2d AKLT-like state at a bulk quantum phasetransition will also be discussed.