Universal Aspects of Quantum Entanglement in Higher Dimensional Disordered Quantum Magnets

纠缠是量子力学的一个显著特征，它提供了比经典物理更强的关联性。然而，我们的知识仍然有限，关于相互作用的量子系统中出现多强的量子关联，特别是在更高的维度。无序量子磁铁不仅与实验相关，而且为测量量子关联的有效计算方法提供了理想的基础。现有的零星的(而且大多是低维的)结果表明，单个子系统的纠缠如何依赖于它的形状，是一个令人惊讶的普遍规律。此外，最近发现，多个子系统之间的纠缠测量在随机量子系统中提供了额外的普遍定律。量子纠缠的这些普遍方面有望在准确定位量子相变以及理解支配普适类方面具有变革性。该项目的目的是在一大类相互作用的高维量子系统中实现对量子纠缠普遍方面的广泛、系统的表征。这一结果将为促进我们对无序量子系统中纠缠的理解提供关键的见解和方法。该项目在物理学、信息论和计算机科学的界面上培训研究生和本科生，为不断发展的劳动力培养不同的独立思考者群体。量子相变是现代物理学的基本问题之一，其性质在固体物理学、量子场论、量子信息学和统计力学中都有研究。量子相变起重要作用的实验例子有稀土磁性绝缘体、重费米子化合物、高温超导体和二维电子气。这项拟议的研究将在相互作用的高维量子系统中形成第一个系统地研究相互作用的高维量子系统中两体和多体水平上纠缠的形状相关的普遍方面。该项目将表征单个扩展或骨架子系统的纠缠熵，以及两个子系统之间的纠缠负性和两个或多个子系统之间的互信息。利用渐近精确的强无序重整化群方法和蒙特卡罗模拟，重点研究了聚合随机横场伊辛模型的临界点和多临界点。这项拟议的研究将极大地扩展现有的文献，并为量子纠缠的普遍方面提供新的见解。所获得的结果和开发的方法在广泛的无序系统中具有潜在的变革性，因为它们提供了定位相变和识别普适性类的有效方法，即使不能访问顺序参数。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Entanglement is a distinguishing property of quantum mechanics, offering fundamentally stronger correlations than classical physics. However, our knowledge remains limited on how strong quantum correlations emerge in interacting quantum systems, especially in higher dimensions. Disordered quantum magnets are not only experimentally relevant, but offer an ideal basis for efficient computational methodologies to measure quantum correlations. The existing, sporadic (and mostly low-dimensional) results indicate surprising, universal laws in how the entanglement of a single subsystem depends on its shape. Moreover, entanglement measures between multiple subsystems were recently found to provide additional universal laws in random quantum systems. Such universal aspects of quantum entanglement are expected to be transformative in pinpointing quantum phase transitions, as well as in understanding the governing universality class. The proposed project aims to achieve an extensive, systematic characterization of the universal aspects of quantum entanglement in a broad class of interacting higher-dimensional quantum systems. The results will provide key insights and methodologies to promote our understanding of entanglement in disordered quantum systems. This project trains graduate and undergraduate students at the interface of physics, information theory, and computer science, preparing a diverse group of independent thinkers for a continuously evolving workforce. Quantum phase transitions are among the fundamental problems of modern physics, the properties of which are studied in solid state physics, quantum field-theory, quantum information and statistical mechanics. Experimental examples in which quantum phase transitions play an important role are, among others, rare-earth magnetic insulators, heavy-fermion compounds, high-temperature superconductors, and two-dimensional electron gases. The proposed research will form the first systematic study of shape-dependent universal aspects of entanglement at the bipartite and multipartite level in interacting higher-dimensional quantum systems. The project will characterize the entanglement entropy of a single extended or skeletal subsystem, as well as the entanglement negativity between two subsystems and the mutual information between two or more subsystems. The focus is on the critical and multicritical points of the paradigmatic random transverse-field Ising model using an efficient implementation of the asymptotically exact strong disorder renormalization group method as well as Monte Carlo simulations. The proposed study will greatly expand the existing literature and provide new insights on universal aspects of quantum entanglement. The obtained results and the developed methodologies are potentially transformative in a broad range of disordered systems, as they provide efficient ways to locate phase transitions and identify universality classes, even without having access to an order parameter.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.