Topological edge states in two-dimensional $\mathbb{Z}_4$ Potts paramagnet protected by the $\mathbb{Z}_4^{\times 3}$ symmetry
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| Format: | Preprint |
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2025
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| _version_ | 1866914212617388032 |
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| author | Topchyan, Hrant Hakobyan, Tigran Mirumyan, Mkhitar Sedrakyan, Tigran A. Sedrakyan, Ara |
| author_facet | Topchyan, Hrant Hakobyan, Tigran Mirumyan, Mkhitar Sedrakyan, Tigran A. Sedrakyan, Ara |
| contents | We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site $G=\mathbb{Z}_4^{\times 3}$ symmetry, starting from a three-component $\mathbb{Z}_4$ Potts paramagnet on a triangular lattice. Within the group-cohomology framework, $H^{3}(G,U(1))\cong \mathbb{Z}_4^{\times 7}$, we focus on a "colorless" cocycle representative obtained by antisymmetrizing the basic $\mathbb{Z}_4$ three-cocycle, and generate the corresponding SPT Hamiltonian via a cocycle-induced nonlocal unitary transformation 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 $\mathbb{Z}_4$ chain with next-to-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 $c=2.191(4)\simeq 11/5$. 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 $\mathbb{Z}_4^{\times 3}$ edge; we outline spectral and symmetry-resolved diagnostics needed to test this identification at the level of conformal towers beyond the central charge. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_18460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological edge states in two-dimensional $\mathbb{Z}_4$ Potts paramagnet protected by the $\mathbb{Z}_4^{\times 3}$ symmetry Topchyan, Hrant Hakobyan, Tigran Mirumyan, Mkhitar Sedrakyan, Tigran A. Sedrakyan, Ara Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site $G=\mathbb{Z}_4^{\times 3}$ symmetry, starting from a three-component $\mathbb{Z}_4$ Potts paramagnet on a triangular lattice. Within the group-cohomology framework, $H^{3}(G,U(1))\cong \mathbb{Z}_4^{\times 7}$, we focus on a "colorless" cocycle representative obtained by antisymmetrizing the basic $\mathbb{Z}_4$ three-cocycle, and generate the corresponding SPT Hamiltonian via a cocycle-induced nonlocal unitary transformation 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 $\mathbb{Z}_4$ chain with next-to-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 $c=2.191(4)\simeq 11/5$. 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 $\mathbb{Z}_4^{\times 3}$ edge; we outline spectral and symmetry-resolved diagnostics needed to test this identification at the level of conformal towers beyond the central charge. |
| title | Topological edge states in two-dimensional $\mathbb{Z}_4$ Potts paramagnet protected by the $\mathbb{Z}_4^{\times 3}$ symmetry |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2512.18460 |