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, Bin-Bin Mao and Zheng Yan ()
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Zhe Wang: School of Science and Research Center for Industries of the Future, Westlake University
Zhiyan Wang: School of Science and Research Center for Industries of the Future, Westlake University
Yi-Ming Ding: School of Science and Research Center for Industries of the Future, Westlake University
Bin-Bin Mao: University of Health and Rehabilitation Sciences
Zheng Yan: School of Science and Research Center for Industries of the Future, Westlake University

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract 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.

Date: 2025
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DOI: 10.1038/s41467-025-61084-7

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