Mathematical aspects of quantum phases of matter

18.07.2021 - 25.07.2021 | Będlewo

The focus of this workshop will be on collective behavior and the underlying mathematical structures of topological and fractonic phases of matter. Quantum phases of matter consist of collective states of particles that have emergent properties beyond their underlying microscopic constituents. The exploration of this exotic realm can lead to deep shifts of the current paradigm and new exciting uses of quantum physics. Quantum phases can be divided by the nature of their excitations with vanishing energy. We distinguish gapped systems that do not have excitations as the energy goes to zero and gapless systems with zero energy excitations in isolated points in momentum space. Examples of gapped systems include insulators and quantum Hall states. Gapless systems comprise of semimetals such as graphene and Dirac/Weyl semimetals or certain newly discovered fractonic phases of matter with immobile excitations. Their exotic properties are believed to be at the heart of new generation of electronics (semimetals) as well as novel type of quantum memories (fractons). Ultimately the research goals are to understand the interplay between symmetry, topology and geometry of quantum matter at different scales.

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