Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation

Based on the recently developed resummation-based quantum Monte Carlo method for the SU(N) spin and loop-gas models, we develop a new algorithm, dubbed ResumEE, to compute the entanglement entropy (EE) with greatly enhanced efficiency. Our ResumEE converts the evaluation of the exponentially small value of the 〈e^{S^(2)})〉, where S^(2) is the 2nd order Rényi EE, to an important sampling process with polynomial accuracy such that the S^(2) for a generic 2D quantum SU(N) spin models can be readily computed without facing the exponential explosion of its variance. We benchmark our algorithm with the previously proposed estimators of S(2) on 1D and 2D SU(2) Heisenberg spin systems to reveal its superior performance and then use it to detect the entanglement scaling data of the Néel-to-VBS transition on 2D SU(N) Heisenberg model with continuously varying N. Our ResumEE algorithm solves the critical problem of precisely evaluating the quantum entanglement in many-body systems and will have a significant impact on reliable access to the conformal field theory data for the highly entangled quantum matter.