Based on the recently developed resummation-based quantum Monte Carlo method for the $\text{SU}(N)$ 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 $\ensuremath{\langle}{e}^{\ensuremath{-}{S}^{(2)}}\ensuremath{\rangle}$, where ${S}^{(2)}$ is the second-order R\'enyi EE, such that the ${S}^{(2)}$ for a generic 2D quantum $\text{SU}(N)$ 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 $\text{SU}(2)$ 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 $\text{SU}(N)$ Heisenberg model with continuously varying $N$ . Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of $\text{SU}(N)$ spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.Based on the recently developed resummation-based quantum Monte Carlo method for the $\text{SU}(N)$ 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 $\ensuremath{\langle}{e}^{\ensuremath{-}{S}^{(2)}}\ensuremath{\rangle}$, where ${S}^{(2)}$ is the second-order R\'enyi EE, such that the ${S}^{(2)}$ for a generic 2D quantum $\text{SU}(N)$ 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 $\text{SU}(2)$ 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 $\text{SU}(N)$ Heisenberg model with continuously varying $N$. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of $\text{SU}(N)$ spin models with continuous $N$ and reliable access to the conformal field theory data for the highly entangled quantum matter.

arXiv:2310.01490Physical review. B./Physical review. BSep 10, 20247 citations

Quantum Monte Carlo Calculations of Entanglement

Norm M. Tubman, Jeremy McMinis

Bulletin of the American Physical SocietyMar 22, 20130 citations

Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative

Zhe Wang, Zhiyan Wang, Yi-Ming Ding +2 more

Entanglement entropy (EE) plays a central role in the intersection of quantum information science and condensed matter physics. However, scanning the EE for two-dimensional and higher-dimensional systems still remains challenging. To address this challenge, we propose a quantum Monte Carlo scheme capable of extracting large-scale data of Rényi EE with high precision and low technical barrier. Its advantages lie in the following aspects: a single simulation can obtain the continuous variation curve of EE with respect to parameters, greatly reducing the computational cost; the algorithm implementation is simplified, and there is no need to alter the spacetime manifold during the simulation, making the code easily extendable to various many-body models. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases. Entanglement entropy is a crucial quantity in several research fields, yet its calculation in higher-dimensional systems remains challenging. Here the authors develop a quantum Monte Carlo-based algorithm to efficiently extract large-scale entanglement entropy data and apply it to quantum critical systems.Entanglement entropy (EE) plays a central role in the intersection of quantum information science and condensed matter physics. However, scanning the EE for two-dimensional and higher-dimensional systems still remains challenging. To address this challenge, we propose a quantum Monte Carlo scheme capable of extracting large-scale data of Rényi EE with high precision and low technical barrier. Its advantages lie in the following aspects: a single simulation can obtain the continuous variation curve of EE with respect to parameters, greatly reducing the computational cost; the algorithm implementation is simplified, and there is no need to alter the spacetime manifold during the simulation, making the code easily extendable to various many-body models. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases. Entanglement entropy is a crucial quantity in several research fields, yet its calculation in higher-dimensional systems remains challenging. Here the authors develop a quantum Monte Carlo-based algorithm to efficiently extract large-scale entanglement entropy data and apply it to quantum critical systems.

arXiv:2406.05324Nature CommunicationsJul 1, 202514 citations

Based on the recently developed resummation-based quantum Monte Carlo method for the

\text{SU}(N)

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 $\ensuremath{\langle}{e}^{\ensuremath{-}{S}^{(2)}}\ensuremath{\rangle}$, where

{S}^{(2)}

is the second-order R\'enyi EE, such that the

{S}^{(2)}

for a generic 2D quantum

\text{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

\text{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

\text{SU}(N)

Heisenberg model with continuously varying

N

. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of

\text{SU}(N)

spin models with continuous

N

and reliable access to the conformal field theory data for the highly entangled quantum matter.