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

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Auteur principal: Corbelli, Matthew
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Publié: 2025
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author Corbelli, Matthew
author_facet Corbelli, Matthew
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_23790
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Symmetry-Compatible Superselection Structures for Product States in 2D Quantum Spin Systems
Corbelli, Matthew
Mathematical Physics
Quantum Physics
81R15
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.
title On Symmetry-Compatible Superselection Structures for Product States in 2D Quantum Spin Systems
topic Mathematical Physics
Quantum Physics
81R15
url https://arxiv.org/abs/2510.23790