This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $330,000 to Yale University to conduct research on quantum phases of matter using symmetry and topology as guiding principles. The award supports three main research thrusts: (1) developing a theory for a new type of non-local observable called the "disorder operator" to probe the fluctuations of symmetry charges; (2) examining the interplay between microscopic conditions and macroscopic observables in lattice quantum systems; and (3) investigating symmetry breaking and topological order in open quantum systems. In addition to the research activities, the award also supports educational and outreach initiatives such as mentoring graduate students, writing review articles, and organizing conferences/workshops. The award period runs from September 1, 2024 to August 31, 2027.
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