Topological and Dynamical Phenomena in Condensed Matter Systems Detected by Quantum Entanglement

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on novel properties of quantum materials and associated phenomena. It has been long recognized that quantum mechanics is essential to understand the basic properties of solids. Understanding the distinction between metals and insulators are one example. With recent advances in experimental techniques, a class of materials has emerged for which subtle quantum effects of the system of their many constituent electrons control macroscopic properties that are characteristic of materials. One example of quantum materials are superconductors. At sufficiently low temperature, a quantum mechanical state forms in which electrons behave collectively leading to conduction of electricity with zero resistance. More recently discovered, is another class of quantum materials that are insulators in their bulk but can support zero resistance conduction of electricity along their surfaces and edges. The metallic surface states in these materials, known as topological insulators, are a consequence of the mathematical structure of the wavefunction which describes the many electron quantum state. The field of mathematics known as topology which focuses on geometric properties of an object that are unchanged by deformations, provides useful ways to describe the structure of the wavefunctions of topological phases in quantum materials. It has become clear that quantum materials can exhibit exotic and surprising properties that do not have a counterpart in ordinary materials. Quantum materials can also host exotic quantum mechanical particles that have intrinsic properties that are quite different from free electrons which make them candidates for the implementation of quantum computers. Novel quantum phenomena can also be found in systems far out of the tranquil state of equilibrium. For example, sufficiently complex quantum many-body systems can "forget" their initial quantum states. In these novel quantum condensed matter systems, quantum entanglement provides a conceptual foundation and tools to study many-body quantum systems. When particles are entangled quantum mechanically, they are connected in a way that affecting one particle will affect all the others, even though they may be separated by vast distances. In this project, the PI aims to develop a deeper theoretical understanding of the properties, including nonequilibrium properties, and phenomena associated with quantum materials, particularly in materials with strongly interacting electrons using concepts such as quantum entanglement together along with others that are associated with the emerging field of quantum information theory. In particular, the PI will examine the nature of the intricate quantum entanglement characteristic of topological phases. He will also investigate how quantum entanglement spreads and propagates in complex many-body quantum systems. A thorough understanding of these problems can pave the way to the discovery of new states of quantum matter and associated phenomena that form the foundations of the next generation of technologies based on quantum mechanics. TECHNICAL SUMMARYThis award supports theoretical research and education with the aim to investigate quantum many-body systems that exhibit novel phenomena, focusing on their topological and far out-of-equilibrium properties. The PI plans to develop a many-body framework to study topological phenomena both in and out of equilibrium, and the structure of multiparty quantum entanglement in topological phases of matter. In particular, the PI plans to construct many-body diagnostics for the topological properties of periodically driven quantum systems in the presence of time-reversal and other symmetries. The PI will seek universal descriptions of quantum information scrambling in complex quantum dynamics using various quantum entanglement measures. To carry out the research, the PI will utilize quantum information theoretical concepts and tools that include quantum entanglement, the channel-state duality, and tensor-networks. The proposed research will lead to a deeper understanding of novel phenomena in quantum many-body systems. The knowledge gained contributes to the foundations of future technological innovations based on quantum mechanical effects. Because of the nature of the proposed work, success in these projects will have impact on many areas of theoretical physics, and may connect to concrete numerical works on model Hamiltonians and experiments in condensed matter systems. Students and young researchers are closely integrated into the research activities and will receive unique training at the frontiers of condensed matter theory.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.