2010/01/31 by Matthew B. Hastings, Ivan Gonzalez, Ann B. Kallin +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevlett.104.157201
published as Phys. Rev. Lett. 104, 157201 (2010) · 4 pages, 4 figures; improved data in fig. 3 and 4, corrected direct swap data in fig. 2
arxiv created 2010/03/03 · arxiv updated 2012/01/18
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 Néel groundstate obeys the expected area law for systems up to linear size L=28.