This 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 SUMMARY
This 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.
Quantum mechanical nature of electrons, combined with strong interactions among them, can lead to exotic behavior. A tantalizing example of this is when confined to two-dimensions and subject to a strong magnetic field, electrons form topologically non-trivial "vacuum" whose "elementary particles" carry charge that is a fraction of that of electron itself, and obey statistics that is neither Bose-Einstein nor Fermi-Dirac. Such "particles", if available and manipulated properly, can be used to build a topological quantum computer. One of the thrust of research supported by this grant is to explore ways to detect and manipulate these exotic particles. We find that a number of conventional thermoelectric and thermodynamic probes are very effective in revealing the presence of such particles and measuring their properties. We further show that in addition to a topological quantum computer, these particles can be used to build a topological quantum refrigerator that can be used to further cool the electrons at very low temperature. Some of our predictions have already led to experimental activity with encouraging outcomes. The origin of such exotic properties is quantum entanglement. We have also studied how to quantify entanglement in many-particle systems, and the origin of certain scaling relations between entanglement and system size. One significant byproduct of this study is an explicit proof that for free fermions, a statistical mechanical description of a small subsystem emerges from such entanglement, even when the whole system is in a pure quantum excited state. The research activity supported by this grant provided valuable training opportunities for graduate students and postdocs. One of the students received his Ph. D. during the funding period. The PI is also writing a modern condensed matter physics textbook, in which research outcomes along the lines described above from the PI as well as the condensed matter physics community at large will be reflected. Such a book will not only help training the next generation of condensed matter physicists, but also informing the broader scientific community as well as general public of exciting developments in our field.
