The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at discovering and understanding new ordered states of matter that arise as a consequence of strong correlations among electrons. This research lies at the interface of theoretical physics and mathematics and often involves synergistically advancing theoretical condensed physics and mathematics in parallel.
The PI will search for new phases of matter. Objectives include: finding and describing phases with topological order, where quasiparticle excitations do not have the quantum numbers of the electron, rather they are "fractionalized;" deriving exact results for particles with non-abelian braiding, where the physics depends on not only which particles are interchanged, but also the order in which they are interchanged; discovering and describing quantum critical points which separate novel phases from phases with conventional order; probing deeply the symmetry structure of one- and two-dimensional models of strongly correlated electrons, in particular the interplay between different competing orders; using integrable field theory in quantum impurity problems, to describe, for example, the observed destruction of coherence by extremely dilute magnetic impurities.
One method utilized will be field theory, especially non-perturbative methods useful for understanding novel phases which cannot be approached by conventional methods. Other methods used include integrability and supersymmetry, which are symmetries making exact computations possible in strongly-correlated systems.
This award supports undergraduate, graduate, and post doctoral education at the interface of theoretical condensed matter physics and mathematics.
NON-TECHNICAL SUMMARY:
The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at discovering and understanding new states of matter and transformations among them. This research lies at the interface of theoretical physics and mathematics and often involves synergistically advancing theoretical condensed physics and mathematics in parallel.
The PI focuses on electrons confined to two-dimensions in a strong magnetic field. Exotic states of matter known are known to exist; the area is ripe for the discovery of more new phases. There is substantial evidence that exotic phases also occur in materials in which the alignment of atomic-scale magnets to produce magnetism on the human scale is "frustrated" often because of the geometric configuration of the atomic-scale magnets on the nanometer scale. One motivation to seek these new phases of matter is to find a system capable of becoming a topological quantum computer. Such a computer could perform certain operations much faster than any currently existing computer. Other unforeseen technologies may also arise. Another motivation is a fundamental understanding of the physical world around whether or not it leads to new technologies, not yet even imagined. The quest leads to the synergistic advance of theoretical condensed matter physics and mathematics.
