Oral: Monte Carlo Measurement of the Renyi Entanglement Entropy for the Fredkin Spin Chain

Calculating the entanglement entropy of the ground states of interesting quantum systems is generally a difficult task that relies on numerical approaches, typically formulated with matrix-product or tensor-network states. We examine the Fredkin spin chain and a family of adjacent quantum spin-1/2 models with three-site interactions. We show that the Rényi entanglement entropies at arbitrary order can be measured stochastically by evaluating an estimator that cyclically permutes spin configurations between multiple Monte Carlo simulation copies across a common cut that cleaves each chain in two. We benchmark our algorithm against exact results at the specially tuned Fredkin point and then calculate the Rényi entanglement entropies for deformations in model space away from the Fredkin point, where analytical results are not available.