Slow Dynamics of the Fredkin Spin Chain

The dynamical behavior of many-particle systems is characterized by the lifetime of quasi-particles or excitations. Observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law ( τ ∼ 1/Δ ~ L^z ). Such decay process are associated with a dynamical exponent (e.g., z = 1 for the ballistic spread of quasi-particles and z = 2 for diffusion) that relates the spread of correlations in space and time. We present numerical results for the Fredkin model---a quantum spin chain with an unusual three-body interaction term---which exhibits a dynamical exponent z ≈ 3. We discuss our efforts to make a reliable, quantitative estimate of z and to explain the very slow dynamics in terms of a random walk executed by the excitation in Monte Carlo time.