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Measuring Renyi Entanglement Entropy with Quantum Monte Carlo · Around

2010

Measuring Renyi Entanglement Entropy with Quantum Monte Carlo

Hastings, Matthew B., Gonzalez, Ivan, Kallin, Ann B. et al.

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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 {\it Swap} operator acting on two copies of the system.

An improved estimator involving the ratio of {\it Swap} operators for different subregions enables simulations to converge the entropy in a 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 groundstate obeys the expected area law for systems up to linear size L=28.

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