Abstract
We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by (×Z3)3 ≡ Z3 × Z3 × Z3 symmetry and smaller Z3 symmetry. We derive microscopic models for the gapless edge, uncover their symmetries and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue, that the low energy limit of our edge modes defined by the SUk(3)/SUk(2) coset conformal field theory with the level k = 2. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.
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Acknowledgments
We are grateful to A. Sedrakyan, H. Babujian, A. Belavin, and A. Litvinov for helpful discussions. We also acknowledge communications from Ryan Lanzetta and Juven Wang with thanks. The research was supported by startup funds from the University of Massachusetts, Amherst (TAS) and Armenian SCS grants Nos. 20TTAT-QTa009 (HT, SK, TH), 20TTWS-1C035 (SK, TH), 21AG-1C024 (HT, MM, SK), and 21AG-1C047 (TH). We are grateful to the anonymous reviewer of JHEP for their insightful comments.
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Topchyan, H., Iugov, V., Mirumyan, M. et al. Z3 and (×Z3)3 symmetry protected topological paramagnets. J. High Energ. Phys. 2023, 199 (2023). https://doi.org/10.1007/JHEP12(2023)199
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DOI: https://doi.org/10.1007/JHEP12(2023)199