Analogies between QFT and lattice systems


Kapustin, A. (2024). Analogies between QFT and lattice systems. Perimeter Institute. https://pirsa.org/24030078


Kapustin, Anton. Analogies between QFT and lattice systems. Perimeter Institute, Mar. 18, 2024, https://pirsa.org/24030078


          @misc{ pirsa_PIRSA:24030078,
            doi = {10.48660/24030078},
            url = {https://pirsa.org/24030078},
            author = {Kapustin, Anton},
            keywords = {Condensed Matter},
            language = {en},
            title = {Analogies between QFT and lattice systems},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030078 see, \url{https://pirsa.org}}

Anton Kapustin California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy


I discuss some analogies between the Haag-Kastler approach to QFT and quantum statistical mechanics of lattice systems. As an illustrative example, I consider the interpretation of the Hall conductance of gapped 2d lattice systems as an obstruction to gauging a global symmetry of a gapped state. I argue that in order to define a proper analog of the net of algebras of observables one needs to study a category of subsets of the lattice equipped with a natural Grothendieck topology.