Schreiber Drinfeld Center as Local Bloch Monodromy

An article that we are finalizing at CQTS:

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• Hisham Sati$\;$and$\;$ Urs Schreiber:

  Drinfeld Center as Quantum State Monodromy

  over Bloch Hamiltonians around Defects

  download: pdf, arXiv:2603.22029

Abstract. The Drinfeld center fusion category $\mathcal{Z}({\mathrm{Vec}_G})$ famously models anyons in certain lattice models. Here we demonstrate how its fusion rules may also describe topological order in fractional topological insulator materials, in the vicinity of point defects in the Brillouin zone.

Concretely, we prove that $\mathcal{Z}({\mathrm{Vec}_G})$ reflects, locally over a punctured disk in the Brillouin zone, the monodromy (topological order) of gapped quantum states over the parameter space of Bloch Hamiltonians whose classifying space has fundamental group $G$.

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