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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