Wang Zhe, Wang Zhiyan, Ding Yi-Ming, Mao Bin-Bin, Yan Zheng
Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, China.
Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, China.
Nat Commun. 2025 Jul 1;16(1):5880. doi: 10.1038/s41467-025-61084-7.
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.
纠缠熵（EE）在量子信息科学与凝聚态物理的交叉领域中起着核心作用。然而，对二维及更高维系统进行纠缠熵扫描仍然具有挑战性。为应对这一挑战，我们提出了一种量子蒙特卡罗方案，该方案能够高精度、低技术门槛地提取雷尼纠缠熵的大规模数据。其优势体现在以下几个方面：单次模拟就能获得纠缠熵随参数的连续变化曲线，大大降低了计算成本；算法实现得到简化，模拟过程中无需改变时空流形，使得代码易于扩展到各种多体模型。此外，我们引入了一个公式，无需从密集的纠缠熵数据进行数值微分就能计算纠缠熵的导数。然后，我们证明了利用纠缠熵及其导数来寻找相变点、临界指数和各种相的可行性。
