Drinfeld Center as Quantum State Monodromy over Bloch Hamiltonians around Defects
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911538272534528 |
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| author | Sati, Hisham Schreiber, Urs |
| author_facet | Sati, Hisham Schreiber, Urs |
| contents | 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 $G$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_22029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Drinfeld Center as Quantum State Monodromy over Bloch Hamiltonians around Defects Sati, Hisham Schreiber, Urs Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V27, 18M20, 81V70, Secondary: 81T45, 55R35, 16T05 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 $G$. |
| title | Drinfeld Center as Quantum State Monodromy over Bloch Hamiltonians around Defects |
| topic | Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V27, 18M20, 81V70, Secondary: 81T45, 55R35, 16T05 |
| url | https://arxiv.org/abs/2603.22029 |