This award supports integrated research, education and outreach activities in theoretical condensed matter physics. The research investigates unconventional phases and phase transitions in strongly correlated fermionic systems. Research is stimulated by the observation that these strong interactions can drive fermionic systems into unconventional phases, that cannot be described by standard paradigms like the Fermi liquid theory. This research undertakes developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, is the central concern of this work.
The research project undertakes specific goals en route to developing the model and theory of such phases and phase transitions. They include: edge states of fractional quantum Hall phase(s) that support quasiparticles with non-Abelian statistics; effects of disorder and finite system size on the properties topological phases in fractional quantum Hall liquids, especially those related to topological quantum computation; ferromagnetic phase and phase transition in one-dimensional metals; unconventional fermionic superfluid phases formed by pairing different species of fermions with density imbalance, and phase transitions among them. 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.
The project employs student researchers who are involved in graduate study in physics. The research contributes to their education in learning the theoretical techniques and understanding the properties of the materials and experience in the use of computational modeling to connect theory to prediction of materials properties. In addition, for the graduate students involved, the research forms the basis for dissertation work leading to the Ph.D.
NON-TECHNICAL SUMMARY:
This award supports integrated research, education and outreach activities in theoretical condensed matter physics. The research investigates unusual ways in which electrons in certain materials can organized themselves. This organization is more subtle than simple spatial organization and half dozen examples of types of orderings involving pair of electrons and there energy states as well as modifications that depend upon the directions in which the electrons spin. Some of these states are well know, including the original BCS state responsible for explaining superconductivity. Other states are merely conjectured.
It is the purpose of the research to investigate and theoretically explain such unusual orderings of electrons in the variety of systems where this has been detected or where it might be detected. This research undertakes developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, is the central concern of this work. Emphasis is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of such unconventional orderings most directly.
The project employs student researchers who are involved in graduate study in physics. The research contributes to their education in learning the theoretical techniques and understanding the properties of the materials and experience in the use of computational modeling to connect theory to prediction of materials properties. In addition, for the graduate students involved, the research forms the basis for dissertation work leading to the Ph.D.
