Highly entangled ground states in 2D

Hamiltonians with unusually high entanglement entropy in the ground states such as deformed colored Motzkin and Fredkin spin chains have been known for several years, however a proper high dimensional generalization of these have not been presented. In this talk I will discuss recent constructions of frustration free Hamiltonians in 2D whose ground states contain extensive entropy. The Hamiltonians are based on decorating height models, such as the six vertex model and the dimer model on the honeycomb lattice with additional degrees of freedom. The constructions feature a deformation parameter that can be tuned to exhibit new phase transitions in the entanglement behavior of the system, namely between perimeter (area) scaling, volume scaling and other intermediate possibilitie.