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We propose a new method to efficiently compute the entanglement entropy (EE)of quantum many-body systems. Our approach, called the incremental SWAPoperator method , combines the simplicity of the SWAP operator used inprojector quantum Monte Carlo simulations with recent advances in preciselycomputing exponential observables using incremental algorithms. We apply thistechnique to obtain accurate EE data at reduced computational cost for 1d and2d antiferromagnetic Heisenberg models with different bipartition schemes.Using the computed EE data, we extract the area law coefficient, universallogarithmic corrections from Goldstone modes, and the geometric constant,finding quantitative agreement with analytical predictions. Moreover, for thefirst time in an unbiased numerical simulation of 2d antiferromagneticHeisenberg model, we successfully obtain reliable universal logarithmiccorrections from sharp corners that match expected theoretical values. Theconsistency between our numerical results and theoretical calculationsdemonstrates the power of our approach for accessing challenging universalentanglement properties. The extensions of our method to other quantumspin/boson models and the interacting fermion models, are outlined.

Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation