Interface, Edge and Bulk of Complex States of Matter

Florida State University, Tallahassee FL

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on exotic properties of many-particle systems with strong interactions. It is known that strong interactions between particles can stabilize various types of phases, which are very different from those familiar from daily life, like solid, liquid and gas. The discovery and understanding of new phases of matter is a central goal of condensed matter physics, which may lead to new technologies; quantum computation might be one example. In addition to directly probing their bulk in theory, the PI and his team will study how to reveal the properties of some of these new phases by probing their edges, as well as the interfaces that separate them. Theoretical results help guide experimental as well as numerical simulations on the same subject. They may also be of interest to researchers in other fields of physics, including high-energy and gravitational physics. Included in this research is the study of some quantum Hall phases, which occur in a two-dimensional sheet of electrons trapped at an interface between semiconductors, cooled to very low temperatures, and placed in an a very strong magnetic field perpendicular to the sheet. The PI will focus on phases that theory suggests exhibit exotic quantum mechanical states the precise nature of which need to be reconciled with experiments. In addition, the research activities supported by this award will introduce graduate students to the frontier of condensed matter physics. Recently the PI has published a new graduate level condensed matter textbook, that reflects the transformative developments of this field over the last few decades. More recently he prepared the solution manual for its homework problems, that has been made available to instructors adopting this book in their teaching. He will continue his work in this direction, including creating and maintaining an online erratum. Such work will further facilitate education of students in this field. TECHNICAL SUMMARY This award supports theoretical research and education on exotic quantum phases of many-particle systems with strong interactions. Some of these phases are of topological nature. One of the main foci of this project is the physical properties of the edges and interfaces separating different topological phases, and their relations to the topological properties of the phases involved. Examples include interfaces between Abelian and non-Abelian quantum Hall phases, and between different non-Abelian phases at the same filling factor but with different topological order. The PI and his team will study both the static and dynamical properties of such interfaces, and the possibility of phase transitions triggered by quantum fluctuations of such interfaces. Another thrust of this project is to view the Fermi surface of gapless fermion systems as a boundary in the phase space, which is a non-commutative; the PI and his team will use the Seiberg-Witten mapping to map such systems to their commutative counterparts and reveal their properties. The PI and his team will use a combination of theoretical and numerical tools in their studies, including density matrix renormalization group, bosonization, and exact diagonalization. They will also attempt to borrow insights and methodology from other fields, including string theory, in which related issues have been studied extensively. These will provide valuable training opportunities for graduate students, as well as stimulating synergy among different fields. In addition, the research activities supported by this award will introduce graduate students to the frontier of condensed matter physics. Recently the PI has published a new graduate level condensed matter textbook, that reflects the transformative developments of this field over the last few decades. More recently he prepared the solution manual for its homework problems, that has been made available to instructors adopting this book in their teaching. He will continue his work in this direction, including creating and maintaining an online erratum. Such work will further facilitate education of students in this field. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.