Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
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arXiv
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| Format: | Preprint |
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2023
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| author | Song, Menghan Wang, Ting-Tung Meng, Zi Yang |
| author_facet | Song, Menghan Wang, Ting-Tung Meng, Zi Yang |
| contents | 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 Rényi 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 Néel-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_01490 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation Song, Menghan Wang, Ting-Tung Meng, Zi Yang Strongly Correlated Electrons Quantum Gases Quantum Physics 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 Rényi 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 Néel-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. |
| title | Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation |
| topic | Strongly Correlated Electrons Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2310.01490 |