Measuring Renyi Entanglement Entropy with Quantum Monte Carlo

Details Measuring Renyi Entanglement Entropy with Quantum Monte Carlo Measuring Renyi Entanglement Entropy with Quantum Monte Carlo

2010-01-13

arxiv.org/abs/1001.2335v2

Phys. Rev. Lett. 104, 157201 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 4 figures; improved data in fig. 3 and 4, corrected direct swap data in fig. 2

Scientific paper

10.1103/PhysRevLett.104.157201

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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