RUI: Numerical Studies of Topological Ordered Phases in Realistic Models

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NONTECHNICAL SUMMARY This award supports theoretical and computational research and education on new electronic states of matter in two-dimensions. Electrons can be confined to two-dimensions within specially made semiconductor devices and in some two-dimensional materials. When a high magnetic field is applied to that electron system at very low temperatures, the fractional quantum Hall effect emerges. In the magnetic field the electrons interact strongly and forgo their individuality: the electron system collectively behaves as if it is comprised of other particles, called anyons, with exotic properties. For example, anyons can appear carrying only a fraction, e.g. one-third of the electron charge. This strange behavior, which fundamentally relies on the cooperation of all the electrons in the system, is a hallmark of a topologically ordered state of matter; their study is currently at the forefront of physics, materials science, and mathematics. A particular type of anyon, called a non-Abelian anyon, has been proposed as a building block for the construction of a quantum computer, a type of computer that is particularly efficient for problems ordinary computers would take an unacceptably long time to solve. Using computer simulations and new theoretical techniques, the PI will address fundamental questions about the experimental realization of non-Abelian anyons in topologically ordered phases. The educational elements will involve modern and exciting research opportunities for the ethnically, culturally, and economically diverse graduate and undergraduate students at the California State University Long Beach (CSULB). The award will aim to recruit more high school students from the greater Los Angeles area to attend CSULB and major in physics or other STEM fields, educate high school teachers about the many interesting facets of condensed matter, and recruit and retain physics majors already enrolled at CSULB. TECHNICAL SUMMARY This award supports theoretical and computational research and education focusing on numerical studies of topologically ordered phases emerging in realistic condensed matter physics models. The research will concentrate on two canonical physical systems: the fractional quantum Hall effect (FQHE), and quantum spin models. Using computationally intensive numerical techniques and advanced theoretical concepts on realistic models, the PI will address central and important questions about the realization of non-Abelian anyons in the FQHE in semiconductor heterostructures and graphene, and the possibility of topologically ordered states in low-dimensional quantum spin models. The PI will resolve questions and stimulate future research in the search for topologically ordered states in realistic systems, contributing to a foundation of knowledge from which to construct a quantum computer. The research questions being addressed in this project are: Do non-Abelian anyonic quasiparticle excitations exist in the FQHE under realistic conditions? Are there topologically ordered phases in realistic low-dimensional quantum spin models, and if so, what is their nature? The educational elements will involve modern and exciting research opportunities for the ethnically, culturally, and economically diverse graduate and undergraduate students at the California State University Long Beach (CSULB). The award will aim to recruit more high school students from the greater Los Angeles area to attend CSULB and major in physics or other STEM fields, educate high school teachers about the many interesting facets of condensed matter, and recruit and retain physics majors already enrolled at CSULB.