近日，印度理工学院的Amit Kumar Pal及其研究团队取得一项新进展。经过不懈努力，他们成功估计二维海森堡模型在强阶耦合极限下的相关性和纠缠度。相关研究成果已于2024年9月9日在国际知名学术期刊《物理评论A》上发表。

该研究团队考虑在任意大小的二维（2D）矩形之字形晶格上，强横档耦合极限下磁场中的各向同性海森堡模型，并利用二阶扰动理论确定了代表二维模型低能态流形的一维（1D）有效模型。

研究人员考虑了在2D模型的希尔伯特空间上定义的若干厄米算符，并系统地推导出它们在低能态流形上的作用，这些作用对应于1D有效模型希尔伯特空间上的算符。对于其中一类算符，研究人员证明了即使在系统参数的扰动区域之外，2D模型低能态流形中计算得到的期望值也可以由1D有效模型中相应算符的期望值来模拟。

研究人员进一步论证，仅在扰动区域内，才可以采用相同的方式定量估计2D模型中基于部分迹的纠缠度量。由于利用具有较小希尔伯特空间的有效1D模型作为代理的优势，这项研究结果和方法预计将在研究具有大系统尺寸的2D模型中的可观测量和纠缠方面发挥重要作用。

附：英文原文

Title: Estimating correlations and entanglement in the two-dimensional Heisenberg model in the strong-rung-coupling limit

Author: Chandrima B. Pushpan, Harikrishnan K J, Prithvi Narayan, Amit Kumar Pal

Issue&Volume: 2024/09/09

Abstract: We consider the isotropic Heisenberg model in a magnetic field in the strong-rung-coupling limit on a two-dimensional (2D) rectangular zig-zag lattice of arbitrary size, and determine the one-dimensional (1D) effective model representing the low-energy manifold of the 2D model up to second order in perturbation theory. We consider a number of Hermitian operators defined on the Hilbert space of the 2D model, and systematically work out their action on the low-energy manifold, which are operators on the Hilbert space of the 1D effective model. For a class of operators among them, we demonstrate that the expectation values computed in the low-energy manifold of the 2D model can be mimicked by the expectation values of the corresponding operators in the 1D effective model even beyond the perturbation regime of the system parameters. We further argue that quantitatively estimating partial trace-based measures of entanglement in the 2D model may be done in the same fashion only in the perturbation regime. Our results and approach are expected to be useful in investigating observables and entanglement in the 2D models with large system sizes due to the advantage of using the effective 1D model with a smaller Hilbert space as a proxy.

DOI: 10.1103/PhysRevA.110.032408

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.032408