Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations.
But as I can see, there are some differences: the ground state of Polyacetelene breaks translational invariance but FQHE does not. In general a symmetry breaking state in 2D are considered as conventional state and does not support fractional excitations.
I wonder why is there such a difference between 1D and 2D fractionalizations?
Is there any 1D model can support fractional excitations from a symmetry preserved ground state ?