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Classifying loops of symmetry-protected states

Mathematical Physics Seminar

Speaker: Sven Bachmann, University of British Columbia
Location: 3204 QMAP
Start time: Mon, Nov 6 2023, 3:10PM

The classification of states of quantum lattice systems is a well-defined mathematical endeavour which started with the discovery of the quantum Hall effect. In this talk, I will discuss the topology of a simple class, the so-called invertible states, which I will define. It is by definition a connected set, and we shall explore its further topological properties. Specifically, I will be interested in what can be identified with its fundamental group; Physically, this is about classifying cycles of physical processes, or pumps. I will present a classification of such loops of invertible state that have a local symmetry, which can be proved to be complete. This is joint work with Wojciech De Roeck, Martin Fraas and Tijl Jappens.