Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
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 {\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.
Cite
@article{arxiv.1001.2335,
title = {Measuring Renyi Entanglement Entropy with Quantum Monte Carlo},
author = {Matthew B. Hastings and Ivan Gonzalez and Ann B. Kallin and Roger G. Melko},
journal= {arXiv preprint arXiv:1001.2335},
year = {2012}
}
Comments
4 pages, 4 figures; improved data in fig. 3 and 4, corrected direct swap data in fig. 2