Connections between entanglement entropy and the height field representation for the Fredkin spin chain

The scaling of entanglement entropy with system size has been the focus of intensive, recent study. In particular, there has been significant effort to find physically plausible systems that violate the area law for entanglement entropy. The Fredkin spin chain, proposed by Salberger and Korepin in 2017, is a gapless, frustration-free spin-1/2 system with three-site interactions that violates the area law logarithmically. The height field representation for the ground state provides a simple graphical method to explore properties of the Fredkin spin chain. We present some preliminary results for the height field statistics as a way to understand the entanglement entropy.