N-ality symmetry and SPT phases in (1+1)d

2025/04/28 by Maeda, Jun, Oishi, Tsubasa · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2504.20151

Abstract

Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying N-ality symmetries, which are a generalization of duality symmetries and are mathematically described by ℤ_N-graded fusion categories. In particular, we focus on an N-ality symmetry obtained by gauging a non-anomalous subgroup of ℤ_N×ℤ_N×ℤ_N symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the N-ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.

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Cited by

• Topological edge states in two-dimensional ℤ₄ Potts paramagnet protected by the ℤ₄^{× 3} symmetry
• Extending fusion rules with finite subgroups: For a general understanding of quotient or gauging
• Noninvertible symmetry and topological holography for modulated SPT in one dimension

Related

• The SymTFT for N-ality defects: Part I
• Duality viewpoint of noninvertible symmetry protected topological phases
• Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry
• Phases with non-invertible symmetries in 1+1D \unicodex2013 symmetry protected topological orders as duality automorphisms
• Exploring G-ality defects in 2-dim QFTs