Very slow spin dynamics in a ferromagnetic chain with three-body interactions

Projector Monte Carlo methods can be adapted to quantum spin models in which the Hamiltonian is a sum of local three-body operators. I discuss the case of spin-half chains whose interactions are pairwise ferromagnetic but contingent on the spin state at a third adjacent site. The resulting family of Hamiltonians, which includes the Fredkin spin chain and its t-deformed cousins, is frustration-free but highly nontrivial. The phase diagram includes states with large entangelement and unusually slow dynamics. Since the Monte Carlo can be carried out independently within each spin sector, I am able to present numerical data for the ground state and various low-lying excitations.