Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian
We systematically study gapless edge modes corresponding to $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases of two-dimensional three-state Potts paramagnets on a triangular lattice. First, we derive microscopic lattice models for the gapless edge and, using the density-matrix renormalizat...
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2025-02-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.2.068 |
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| author | Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran Hakobyan, Tigran A. Sedrakyan, Ara G. Sedrakyan |
| author_facet | Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran Hakobyan, Tigran A. Sedrakyan, Ara G. Sedrakyan |
| author_sort | Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran Hakobyan, Tigran A. Sedrakyan, Ara G. Sedrakyan |
| collection | DOAJ |
| description | We systematically study gapless edge modes corresponding to $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases of two-dimensional three-state Potts paramagnets on a triangular lattice. First, we derive microscopic lattice models for the gapless edge and, using the density-matrix renormalization group (DMRG) approach, investigate the finite-size scaling of the low-lying excitation spectrum and the entanglement entropy. Based on the obtained results, we identify the universality class of the critical edge, namely the corresponding conformal field theory and the central charge. Finally, we discuss the inherent symmetries of the edge models and the emergent winding number symmetry. As a result, one-dimensional chains with this symmetry form a model that supports gapless excitations due to its tricritical symmetry. Numerically, we show that low-energy states in the continuous limit of the edge model can be described by conformal field theory (CFT) with central charge $c=1$, given by the coset $SU_k(3)/SU_k(2)$ CFT at level k=1. |
| format | Article |
| id | doaj-art-e964c9215ce74eec822d1296d29cedfc |
| institution | DOAJ |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-e964c9215ce74eec822d1296d29cedfc2025-08-20T03:11:03ZengSciPostSciPost Physics2542-46532025-02-0118206810.21468/SciPostPhys.18.2.068Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary HamiltonianHrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran Hakobyan, Tigran A. Sedrakyan, Ara G. SedrakyanWe systematically study gapless edge modes corresponding to $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases of two-dimensional three-state Potts paramagnets on a triangular lattice. First, we derive microscopic lattice models for the gapless edge and, using the density-matrix renormalization group (DMRG) approach, investigate the finite-size scaling of the low-lying excitation spectrum and the entanglement entropy. Based on the obtained results, we identify the universality class of the critical edge, namely the corresponding conformal field theory and the central charge. Finally, we discuss the inherent symmetries of the edge models and the emergent winding number symmetry. As a result, one-dimensional chains with this symmetry form a model that supports gapless excitations due to its tricritical symmetry. Numerically, we show that low-energy states in the continuous limit of the edge model can be described by conformal field theory (CFT) with central charge $c=1$, given by the coset $SU_k(3)/SU_k(2)$ CFT at level k=1.https://scipost.org/SciPostPhys.18.2.068 |
| spellingShingle | Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran Hakobyan, Tigran A. Sedrakyan, Ara G. Sedrakyan Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian SciPost Physics |
| title | Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian |
| title_full | Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian |
| title_fullStr | Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian |
| title_full_unstemmed | Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian |
| title_short | Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian |
| title_sort | two dimensional topological paramagnets protected by mathbb z 3 symmetry properties of the boundary hamiltonian |
| url | https://scipost.org/SciPostPhys.18.2.068 |
| work_keys_str_mv | AT hranttopchyanvasiliiiugovmkhitarmirumyantigranhakobyantigranasedrakyanaragsedrakyan twodimensionaltopologicalparamagnetsprotectedbymathbbz3symmetrypropertiesoftheboundaryhamiltonian |