PIRSA:24030078 Conference Condensed Matter

DOI10.48660/24030078

Conference/School: Higher Categorical Tools for Quantum Phases of Matter

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}}
}

Abstract

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.

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