Disentangling modular WalkerWang models via fermionic invertible boundaries
Abstract
WalkerWang models are fixedpoint models of topological order in $3+1$ dimensions constructed from a braided fusion category. For a modular input category $\mathcal M$, the model itself is invertible and is believed to be in a trivial topological phase, whereas its standard boundary is supposed to represent a $2+1$dimensional chiral phase. In this work we explicitly show triviality of the model by constructing an invertible domain wall to vacuum as well as a disentangling local unitary circuit in the case where $\mathcal M$ is a Drinfeld center. Moreover, we show that if we allow for fermionic (auxiliary) degrees of freedom inside the disentangling domain wall or circuit, the model becomes trivial for a larger class of modular fusion categories, namely those in the Witt classes generated by the Ising UMTC. In the appendices, we also discuss general (noninvertible) boundaries of general WalkerWang models and describe a simple axiomatization of extended TQFT in terms of tensors.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.03397
 Bibcode:
 2022arXiv220803397B
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Mathematics  Quantum Algebra;
 Quantum Physics
 EPrint:
 v2: Improvements in appendix B