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Topological edge states in two-dimensional Z4 Potts paramagnet protected by the Z4×3 symmetry

Hrant Topchyan1, Tigran Hakobyan1,2, Mkhitar Mirumyan1, Tigran A. Sedrakyan1,3, and Ara Sedrakyan1

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Phys. Rev. B 114, 065111 – Published 8 July, 2026

DOI: https://doi.org/10.1103/xszt-gsss

Abstract

We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site G=Z4×3 symmetry, starting from a three-component Z4 Potts paramagnet on a triangular lattice. Within the group-cohomology framework, H3[G,U(1)]≅Z4×7, we focus on a colorless cocycle representative obtained by antisymmetrizing the basic Z4 three-cocycle, and generate the corresponding SPT Hamiltonian via a cocycle-induced local unitary transformation H3[G,U(1)]≅Z4×7 followed by symmetry averaging. For open geometry, we derive the boundary theory explicitly: one color sector decouples, while the nontrivial edge reduces to an interacting Z4 chain with next-nearest-neighbor constraints that admits a compact dressed-Potts form. Using DMRG we show that the boundary model is gapless, with the lowest gap scaling as 1/L and an entanglement-entropy scaling consistent with a conformal field theory of central charge c=2.191(4)≃11/5. The rational value c=11/5 matches the coset SU(3)3/SU(2)3, making it a candidate for the continuum description of the Z4×3 edge; we outline spectral and symmetry-resolved diagnostics needed to test this identification at the level of conformal towers beyond the central charge.

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Outline

Information

Phys. Rev. B 114, 065111– Published 8 July, 2026
  • Received 30 December 2025
  • Revised 15 May 2026
  • Accepted 16 June 2026
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