CAREER: Quantum Fluctuations, Entanglement and the Casimir Effect

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TECHNICAL SUMMARY This CAREER award supports theoretical research that draws upon methods of mathematical physics and field theory to address fundamental features of quantum fluctuations in condensed matter physics and their interplay with geometry. The research intersects condensed matter physics, mathematical physics, and quantum information theory. The research has three main thrusts, each of which involves developing new methods and ideas: 1) The entanglement structure of many-body states with a special focus on condensed matter systems, such as topological insulators and quantum Hall states. This includes entanglement scaling and spectrum. 2) Quantum fluctuations and their interplay with boundaries through the Casimir effect. This includes research into the role of matter radiation entanglement and the direction of Casimir forces in the presence of dissipative materials. 3) Topological states and their interplay with fluctuations. Such a study is of great interest for its crucial importance to the idea of topological quantum computation. The scientific broader impact of the proposed research is to advance integration between branches of theoretical physics such as quantum field theory, statistical mechanics, and quantum information theory with mathematically active areas such as topology and functional analysis in order to enrich both disciplines and to unravel the connections between them. Furthermore, the research is related to ongoing experimental efforts at the forefront of modern physics. For example, the study of Casimir forces is projected to be of fundamental importance when designing nano-mechanical structures. Topological phases have potential application in topological quantum computing and are expected to exist in fractional quantum hall systems. The educational component involves introducing graduate students to modern problems in theoretical condensed matter through the introduction of new and exciting problems and techniques. The PI will write an upper undergraduate to graduate level textbook on the Casimir effect from a condensed matter perspective. NON-TECHNICAL SUMMARY This CAREER award supports theoretical research that draws on advanced physical and mathematical concepts and theoretical methods to advance our understanding of (i) topological insulators, which are materials that cannot conduct electricity in their interior but allow movement of charges on their edges or boundaries, (ii) Casimir effect, a quantum mechanical effect that leads to attraction between two very closely spaced metallic plates in vacuum, even though they have no electric charge, and (iii) topological phases, which are new states of matter which may hold the key to making a fault-tolerant quantum computer expected to be much faster than its classical counterpart. This research is connected to ongoing experimental efforts at the forefront of modern physics. For example, Casimir forces are expected to be more important as the physical dimensions of devices and mechanisms approach dimensions some 100,000 times smaller than a human hair. The educational component involves introducing graduate students to modern problems in theoretical condensed matter through the introduction of new and exciting problems and techniques. The PI will write an upper undergraduate to graduate level textbook on the Casimir effect from a condensed matter perspective.