Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations

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Abstract
We develop a quantum Monte~Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary Swap operator acting on two copies of the system. An improved estimator involving the ratio of Swap operators for different subregions enables convergence of the entropy in a simulation time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the N\'eel ground state obeys the expected area law for systems up to linear size L=32.

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