Universal Aspects of Quantum Entanglement in Higher Dimensional Disordered Quantum Magnets

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.