This CAREER award supports theoretical research and education towards investigating possible states of matter that can appear in solid-state materials. One of the ultimate goals of condensed matter physics is to theoretically understand and realize in the laboratory all possible phases of matter. The traditional approach to distinguishing different phases of matter from one another is based on ideas of symmetry. For instance, different solids can be classified by the distinct crystal symmetries the atoms that form them attain, e.g. cubic. A similar approach can also be applied to the many phases interacting electrons can create in materials.
However, that approach is essentially based on intuition from classical physics and is in practice insufficient for describing a multitude of phases of matter enabled by quantum mechanics. In fact, that approach does not even allow one to theoretically distinguish a metal from an insulator. Even more surprising, there exist distinct insulators with the same symmetry. The central goal of this project is the study of these quantum insulators and the vast array of phenomena they host, which include surfaces on which electric conduction protected from the usually detrimental effects of material disorder exists. Such understanding could lead to general conclusions about the complex behavior of electrons in materials and could eventually provide material platforms for the building blocks of quantum computers.
Beyond its own field, this project can have impact on several other areas of science, such as mathematics and high-energy physics. In addition to the research, the project includes a multipronged educational and outreach program targeting K-12, undergraduate, and graduate students. The K-12 community will be reached through participation in the NSF-funded Theorynet program that brings theorists into classrooms, and through co-organization of the Boston Physics Circle, which prepares high-school students for physics competitions. The undergraduate community will be served by direct involvement in research and by popular research presentations. A major component of this project is the training of graduate students who will be involved in all aspects of the research.
This CAREER award supports theoretical research and education towards understanding fundamentals of strongly interacting electron systems. In the last decade there has been an impressive progress in the understanding of gapped phases of matter. Ideas of symmetry and topology play an important role in the physics of such phases. Part of the progress has been driven by the study of symmetry-protected topological (SPT) phases, which are interacting generalizations of topological insulators.
Much of the interesting physics of an SPT occurs at its boundary, which is guaranteed to carry nontrivial symmetry-protected edge modes. Surprisingly, a full classification of SPT phases of bosons and, more recently, fermions with arbitrary interactions has been proposed. However, the understanding of surface states of such phases is still limited, particularly for strongly interacting SPT phases of fermions. The study of boundaries of 2D and 3D SPTs and the application of results to other problems is a major goal of this project. In particular, the PI will investigate: i) Gapped symmetric boundaries of 3D SPTs supporting anyon excitations, ii) 2D fermion SPTs and their 1D CFT boundaries, iii) Application of SPTs to derive tight electron filling constraints on the existence of (interacting) insulators in 3D, iv) SPT surface states in the presence of quenched disorder.
This research will significantly advance our understanding of strongly interacting phases of matter (beyond just SPTs). In particular, it will deepen our understanding of symmetry anomalies, which may lead to the conjecture of new dualities between quantum field theories.
Beyond its own field, this project can have impact on several other areas of science, such as mathematics and high-energy physics. In addition to the research, the project includes a multipronged educational and outreach program targeting K-12, undergraduate, and graduate students. The K-12 community will be reached through participation in the NSF-funded Theorynet program that brings theorists into classrooms, and through co-organization of the Boston Physics Circle, which prepares high-school students for physics competitions. The undergraduate community will be served by direct involvement in research and by popular research presentations. A major component of this project is the training of graduate students who will be involved in all aspects of the research.
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.
