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 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.
Hastings
Matthew B
MB
Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California 93106, USA.
González
Iván
I
Kallin
Ann B
AB
Melko
Roger G
RG