Slow dynamics of the Fredkin spin chain

TL;DR

This paper investigates the slow, anomalous dynamics of the Fredkin spin chain, revealing a large dynamical exponent and explaining the slow relaxation through constrained random walk behavior of excitations.

Contribution

It provides the first detailed numerical estimate of the dynamical exponent for the Fredkin model and links slow dynamics to constrained random walk excitations.

Findings

Dynamical exponent z ≈ 3.16 determined through simulations

Fredkin model exhibits unusually slow relaxation dynamics

Slow dynamics explained by constrained random walk of excitations

Abstract

The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law. Such processes are associated with a dynamical exponent $z$ that relates the spread of correlations in space and time. We present numerical results for the Fredkin model, a quantum spin chain with a three-body interaction term, which exhibits an unusually large dynamical exponent. We discuss our efforts to produce a reliable estimate $z$=3.16(1) through direct simulation of the quantum evolution and to explain the slow dynamics in terms of an excited bond that executes a constrained random walk in Monte Carlo time.