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Condensed Matter > Strongly Correlated Electrons
Title: Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
(Submitted on 2 Oct 2023 (v1), last revised 27 May 2024 (this version, v4))
Abstract: 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 exponentially speeds up the computation of the exponentially small value of the $\langle e^{-S^{(2)}}\rangle$, where $S^{(2)}$ is the 2nd order R\'enyi EE, such that the $S^{(2)}$ for a generic 2D quantum SU($N$) spin models can be readily computed with high accuracy. 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 N\'eel-to-VBS transition on 2D SU($N$) Heisenberg model with continuously varying $N$. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of SU($N$) spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.
Submission history
From: Menghan Song [view email][v1] Mon, 2 Oct 2023 18:00:02 GMT (3862kb,D)
[v2] Wed, 4 Oct 2023 03:52:56 GMT (3862kb,D)
[v3] Wed, 18 Oct 2023 12:15:38 GMT (3862kb,D)
[v4] Mon, 27 May 2024 03:19:17 GMT (3807kb,D)
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