Exact Holographic Tensor Networks

We present exact holographic tensor network representations for a class of ground states of a continuous family of frustration-free Hamiltonians.
These states, known as area deformed Motzkin states, exhibit a novel quantum phase transition where the entanglement entropy transitions continuously from being bounded to scaling with the volume.
The states provide a test case for recent ideas about holography interpreted as an optimized path integral representation of a state.
In particular, by tuning the parameter we can go from the highly entangled ``Rainbow'' phase where no tree representation (such as MERA) is possible for the state to a Lifshitz point where we present a tree-like structure for the ground state.