Measuring Renyi entanglement entropy in quantum Monte Carlo simulations

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 differe...

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Bibliographic Details
Published in:Physical review letters 2010-04, Vol.104 (15), p.157201-157201, Article 157201
Main Authors: Hastings, Matthew B, González, Iván, Kallin, Ann B, Melko, Roger G
Format: Article
Language:English
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Summary: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 Néel ground state obeys the expected area law for systems up to linear size L=32.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.104.157201