Universal Aspects of Quantum Entanglement in Higher Dimensional Disordered Quantum Magnets

纠缠是量子力学的一个显著特性，它提供了比经典物理更强的相关性。然而，我们的知识仍然有限，在相互作用的量子系统中，特别是在更高的维度中，量子关联有多强。无序量子磁体不仅与实验相关，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（大多是低维的）结果表明，令人惊讶的，普遍的法律，如何纠缠的一个单一的子系统取决于它的形状。此外，最近发现多个子系统之间的纠缠度量可以为随机量子系统提供额外的普适定律。量子纠缠的这种普遍性方面预计将在精确定位量子相变方面具有变革性，以及在理解支配普遍性类方面具有变革性。拟议的项目旨在实现一个广泛的，系统的表征量子纠缠的普遍方面在一个广泛的相互作用的高维量子系统。这些结果将为我们理解无序量子系统中的纠缠提供关键的见解和方法。该项目培养研究生和本科生在物理学，信息理论和计算机科学的接口，准备一个独立的思想家为不断发展的劳动力的多元化群体。 量子相变是现代物理学的基本问题之一，其性质在固态物理、量子场论、量子信息和统计力学中进行研究。量子相变在实验中扮演重要角色的例子包括稀土磁性绝缘体、重费米子化合物、高温超导体和二维电子气。拟议的研究将形成在相互作用的高维量子系统中，在二分和多分水平上对纠缠的形状依赖的普遍方面的第一个系统性研究。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。重点是临界点和多临界点的范例随机横场伊辛模型使用的渐近精确的强无序重整化群方法以及蒙特卡罗模拟的有效实施。这项研究将极大地扩展现有文献，并为量子纠缠的普遍性提供新的见解。所获得的结果和开发的方法是潜在的变革，在广泛的无序系统，因为它们提供了有效的方法来定位相变和识别普适类，即使没有访问的顺序parameter.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.