arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节（Veterans Day），12 日无更新
arXiv 2410.00515quant-phcond-mat.dis-nncond-mat.str-el
收藏

探索具有简并基态的有限尺寸量子系统中的纠缠

Exploring entanglement in finite-size quantum systems with degenerate ground state

V. S. Okatev, O. M. Sotnikov, V. V. Mazurenko

发表信息：
Physical Review B 111, 054443 (2025)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文提出一种利用 Haar 测度生成随机线性组合并估算 von Neumann 熵的方法，用于表征简并基态自旋系统中的非局域量子关联，并通过数字量子模拟验证了该方法在噪声下对纠缠描述的准确性。

摘要：

我们开发了一种方法，用于表征具有精确或近似简并基态的自旋系统中的非局域量子关联。从通过精确对角化计算出的线性无关的简并本征函数出发，我们生成了它们的一组有限随机线性组合，并采用 Haar 测度，这保证了这些组合在初始本征态所张成的空间中均匀分布。估算随机波函数的 von Neumann 熵有助于揭示基态简并相中量子关联此前未知的特征。例如，具有 Dzyaloshinskii-Moriya 相互作用的量子磁体的自旋螺旋相以纠缠熵的增强为特征，这可以通过双自旋和三自旋关联函数的行为变化来定性解释。为了建立理论发现与真实实验之间的联系，我们深入探讨了基于对大量简并本征态的单次测量来估算可观测量的问题。通过求解简单 Ising 模型的例子表明，使用量子计算机执行的数字量子模拟即使在存在噪声的情况下，也能提供对简并系统纠缠的准确描述。我们还讨论了简并费米子和玻色子模型的基态性质，这对于超冷原子实验的理论分析可能很有用。

英文摘要：

We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states. Starting with linearly independent degenerate eigenfunctions calculated with exact diagonalization we generate a finite set of their random linear combinations with Haar measure, which guarantees that these combinations are uniformly distributed in the space spanned by the initial eigenstates. Estimating the von Neumann entropy of the random wave functions helps to reveal previously unknown features of the quantum correlations in the phases with degeneracy of the ground state. For instance, spin spiral phase of the quantum magnet with Dzyaloshinskii-Moriya interaction is characterized by the enhancement of the entanglement entropy, which can be qualitatively explained by the changes in behaviour of two- and three-spin correlation functions. To establish the connection between our theoretical findings and real experiments we elaborate on the problem of estimating observables on the basis of the single-shot measurements of numerous degenerate eigenstates. By the example of solving a simple Ising model it is shown that digital quantum simulations performed with quantum computers can provide accurate description of the entanglement of the degenerate systems even in the presence of noise. We also discuss the ground state properties of degenerate fermionic and bosonic models, which can be useful for theoretical analysis of the experiments with ultracold atoms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑