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Topological and nontopological degeneracies in generalized string-net models | | Anna Ritz-Zwilling
; Jean-Noël Fuchs
; Steven H. Simon
; Julien Vidal
; | | Date: |
1 Sep 2023 | | Abstract: | Generalized string-net models have been recently proposed in order to enlarge
the set of possible topological quantum phases emerging from the original
string-net construction. In the present work, we do not consider vertex
excitations and restrict to plaquette excitations, or fluxons, that satisfy
important identities. We explain how to compute the energy-level degeneracies
of the generalized string-net Hamiltonian associated to an arbitrary unitary
fusion category. In contrast to the degeneracy of the ground state, which is
purely topological, that of excited energy levels depends not only on the
Drinfeld center of the category, but also on internal multiplicities obtained
from the tube algebra defined from the category. For a noncommutative category,
these internal multiplicities result in extra nontopological degeneracies. Our
results are valid for any trivalent graph and any orientable surface. We
illustrate our findings with nontrivial examples. | | Source: | arXiv, 2309.00343 | | Services: | Forum | Review | PDF | Favorites | |
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