Unconventional Phases and Phase Transitions in Electronic and Trapped Cold Atom Systems

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TECHNICAL SUMMARYThis award supports integrated research and education in theoretical condensed matter physics. The PI aims to investigate unconventional phases and phase transitions in strongly correlated electronic and cold atom systems. The research is motivated by the observation that strong interactions can drive these systems into unconventional phases, which cannot be described by standard paradigms like the Fermi liquid theory. The PI will undertake specific goals en route to developing models and theories of unconvetional phases and phase transitions. They include: Unusual bulk and edge properties of fractional quantum Hall phase(s) that support quasiparticles with non-Abelian statistics; cold atom systems that support various types of fractional quantum Hall phase(s) and undergo quantum phase transitions between them; exotic phases formed by mixtures of bosonic and fermionic atoms/molecules; and excitonic states formed by pairing particles and holes in semiconductors. All of these phases and phase transitions are currently being studied very actively by both experimentalists and theorists. Various analytical and numerical methods will be used in the theoretical studies proposed here. Specific methods include bosonization, renormalization group, particle-vortex duality transformation, exact diagonalization, and numerical implementation of mean-field theories. Emphasis is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of such unconventional phases most directly.This project provides educational opportunities for graduate student and postdoctoral researchers to learn advanced theoretical techniques and computational methods. The PI will also be heavily involved in various services to the scientific community, including organizing national and international professional conferences.NONTECHNICAL SUMMARYThis award supports integrated research and education in theoretical condensed matter physics. The PI aims to investigate unusual ways in which electrons and atoms in certain materials can organize themselves. This organization is more subtle than simple spatial organization, such as the regular periodic array of atoms in a crystal. Some of these states are well known, including the original Bardeen, Cooper, and Schrieffer state for superconductivity, a state of matter that can conduct electricity without dissipation. Other states are predictions. The PI will investigate and theoretically explain such unconventional ordering of electrons and atoms in a variety of materials where it might be detected. This research involves developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, as its central goal. Emphasis is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of unconventional order most directly.This project provides educational opportunities for graduate student and postdoctoral researchers to learn advanced theoretical techniques and computational methods. The PI will also be heavily involved in various services to the scientific community, including organizing national and international professional conferences.