Deformed Fredkin Spin Chain with Extensive Entanglement

Understand

We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling.

• In this chain, spins have a local interaction of three nearest neighbors.
• The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths.
• In the purely spin $1/2$ case, the entanglement entropy obeys an area law: it is bounded from above by a constant, when the size of the block $n$ increases (and $t>1$).