Matthew Corbelli | Searcharxiv

arXiv2025

On Symmetry-Compatible Superselection Structures for Product States in 2D Quantum Spin Systems

We study superselection sectors in two-dimensional quantum spin systems with an on-site action of a compact abelian group $G$. Naaijkens and Ogata (2022) arXiv:2102.07707 showed that for states quasi-equivalent to a product state, the superselection structure is trivial, reflecting the absence of long-range entanglement. We consider a symmetry-compatible refinement of this setting, in which both the superselection criterion and the notion of equivalence between representations are required to respect the $G$-action. Under this stricter notion of equivalence, the sector structure for a $G$-equivariant product representation becomes nontrivial: the $G$-equivariant superselection sectors are classified by elements of the Pontryagin dual $\widehat{G}$. This shows that even in phases without long-range entanglement, imposing symmetry compatibility can lead to nontrivial sector structure.

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arXiv2024

Tensor category describing anyons in the quantum Hall effect and quantization of conductance

In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume ground state. While Hall conductance is well-defined in this scenario, existing proofs of its quantization have relied on assumptions of either weak interactions, or properties of finite volume ground state spaces, or invertibility. Here, we assume that the conditions necessary to construct the braided $C^*$-tensor category which describes anyonic excitations are satisfied, and we demonstrate that the Hall conductance is rational if the tensor category is finite.

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