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Hamiltonian models for topological phases of matter in three spatial dimensions
- Autor(en)
- Dominic J. Williamson, Zhenghan Wang
- Abstrakt
We present commuting projector Hamiltonian realizations of a large class of (3 + 1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the Crane-Yetter-Walker-Wang and 2-Group gauge theory models. We also present Hamiltonian realizations of a state sum TQFT recently constructed by Kashaev whose relation to existing models was previously unknown. We argue that this TQFT is captured as a special case of the Crane-Yetter-Walker-Wang model, with a premodular input category in some instances.
- Organisation(en)
- Quantenoptik, Quantennanophysik und Quanteninformation
- Externe Organisation(en)
- Microsoft Research, University of California, Santa Barbara
- Journal
- Annals of Physics
- Band
- 377
- Seiten
- 311-344
- Anzahl der Seiten
- 34
- ISSN
- 0003-4916
- DOI
- https://doi.org/10.1016/j.aop.2016.12.018
- Publikationsdatum
- 02-2017
- Peer-reviewed
- Ja
- ÖFOS 2012
- 103024 Quantenfeldtheorie, 103019 Mathematische Physik
- Schlagwörter
- ASJC Scopus Sachgebiete
- Allgemeine Physik und Astronomie
- Link zum Portal
- https://ucrisportal.univie.ac.at/de/publications/3cce4096-6b53-4600-ad1c-fdb05b39016d