CAREER: Geometric Quantum Order: Fractons, Tensor Gauge Theories and Beyond

Brown University, Providence RI

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports joint theoretical research and education to advance the theoretical foundations of condensed matter physics. Condensed matter physics concerns itself with systems composed of a large number of interacting constituents. Materials are a common example as they contain many atoms and many electrons. It is common to think of such complex systems not in terms of the individual constituents, but rather in terms of properties that emerge from their collective behavior. The concept of phases of matter is an important example of a collective property. Systems that show the same phase have similar properties. Ferromagnets have the collective property that the constituent atoms or electrons align in such a way that the magnetic axis of each one points in the same direction. Ferromagnets made of different materials are all ferromagnets. However, a ferromagnet is qualitatively different from an antiferromagnetic phase in which the magnetic axis of one atom points in the direction opposite that of its neighbor. So, systems that belong to the same phase have similar qualitative properties, while systems that belong to different phases have different properties. When quantum mechanics mingles with strong interactions among constituents very strange phases can emerge, such as the topological phases of the fractional quantum Hall effect; the latter occurs when electrons confined to a two-dimension plane by semiconductors are exposed to an intense magnetic field. Recently proposed fracton phases of matter are another turning point in this development. These phases have the interesting and distinct property of being hypersensitive to the geometry of the underlying material, for example the way atoms are organized on a lattice, as well as the presence of geometric distortions of the lattice. The PI will undertake a careful study and characterization of these phases, which necessitates the development new concepts and new theoretical tools. New tools will help advance understanding of the physical properties of fracton phases as well as suggest routes for experimental detection of fractions in materials. This is fundamental research; however, fractons could play an important role in developing quantum memory, and suggest new ways to think about quantum computing. Finally, it is already becoming clear that some fracton phenomena may have been discovered long ago in superfluids and liquid crystals, without realizing that these are but a page of a much bigger story. The PI will utilize the new techniques developed in the fracton context to gain new insights into the problems of vortices in superconductors, turbulence, and quantum liquid crystals. The education component of this CAREER project includes training undergraduate and graduate students. Students will explore how to use machine learning methods to gain insight into theoretical problems. The PI will participate in global efforts to increase diversity in physics through mentoring undergraduate students who are members of underrepresented groups leveraging American Physical Society initiatives. The PI will engage in outreach in local high schools by participating in career days and encouraging students to study science. PI will develop a course aimed at undergraduate and graduate students that will focus on applications of condensed matter physics ideas to deep neural networks. TECHNICAL SUMMARY This CAREER award supports joint theoretical research and education to advance the theoretical foundations of strongly correlated topological and geometric phases of matter. The project is focused on the physics of systems that support emergent fracton excitations. These excitations possess two remarkable properties: (i) they are topologically non-trivial and (ii) they cannot freely move through space. The constraints on their motion arise dynamically, while the underlying physical system is translation invariant. More concretely the research concentrated on three major efforts. (i) Fracton excitations can emerge in gapless correlated spin liquids. The PI will explore how the existence of these excitations affects observable properties of these systems. (ii) The constrained mobility of fracton excitations can be formally imposed by introducing additional symmetries. The variety of all possible mobility constraints roughly corresponds to all possible symmetries of this kind. The PI will develop a general theory of such symmetries and their manifestation in low energy properties of the physical systems constrained by these symmetries. (iii) A particular form of fracton behavior is already present in well-known systems such as superfluids, liquid crystals and quantum Hall states, where vortices, crystalline defects and composite fermions have a subtle version of constrained motion. The PI will investigate this tantalizing connection with the expectation that fracton machinery will provide a fresh look at these systems. The education component of this CAREER project includes training undergraduate and graduate students. Students will explore how to use machine learning methods to gain insight into theoretical problems. The PI will participate in global efforts to increase diversity in physics through mentoring undergraduate students who are members of underrepresented groups leveraging American Physical Society initiatives. The PI will engage in outreach in local high schools by participating in career days and encouraging students to study science. PI will develop a course aimed at undergraduate and graduate students that will focus on applications of condensed matter physics ideas to deep neural networks. 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.