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