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 studies the edge states at the 1d boundary of 2d
strongly interacting symmetry protected topological (SPT) states,
when the bulk is driven to a disorder-order phase transition. We
will take the 2d Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an
example, which is a SPT state protected by the SO(3) spin
symmetry and spatial translation. We found that the original
(1+1)d boundary conformal field theory of the AKLT state is
unstable due to coupling to the boundary avatar of the bulk
quantum critical fluctuations. When the bulk is fixed at the
quantum critical point, within the accuracy of our expansion
method, we find that by tuning one parameter at the boundary,
there is a generic direct transition between the long range
antiferromagnetic Néel order and the valence bond solid (VBS)
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. Connections between our
analytical studies and recent numerical results concerning the
edge states of the 2d AKLT-like state at a bulk quantum phase
transition will also be discussed.
Microscopic analysis of the superconducting quantum critical point: Finite-temperature crossovers in transport near a pair-breaking quantum phase transition
