Resummation-based quantum Monte Carlo for entanglement entropy computation

Based on the recently developed resummation-based quantum Monte Carlo method for the $\text{SU}\left(N\right)$ spin and loop-gas models, we developed an algorithm, dubbed ResumEE, to compute the entanglement entropy (EE) with greatly enhanced efficiency. Our ResumEE exponentially speeds up the computation of the exponentially small value of the $〈e^{-S^{\left(2\right)}}〉$, where $S^{\left(2\right)}$ is the second-order Rényi EE, such that the $S^{\left(2\right)}$ for a generic 2D quantum $\text{SU}\left(N\right)$ spin models can be readily computed with high accuracy. We benchmark our algorithm with the previously proposed estimators of $S^{\left(2\right)}$ on 1D and 2D $\text{SU}\left(2\right)$ 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 $\text{SU}\left(N\right)$ Heisenberg model with continuously varying $N$. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of $\text{SU}\left(N\right)$ spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.