Quantum phase transition from bounded to extensive entanglement entropy   in a frustration-free spin chain
  We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the {ground state of our model is non-degenerate and exhibits} a novel quantum phase transition from bounded entanglement entropy to a massively entangled state with volume entropy scaling. The ground state may be interpreted as a deformation away from the uniform superposition of colored Motzkin paths, showed by Movassagh and Shor to have a large (square-root) but sub-extensive scaling of entanglement into a state with an extensive entropy. 
Zhao Zhang, Amr Ahmadain and Israel Klich
quant-ph cond-mat.stat-mech math-ph math.MP