TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.2.068
TI  - Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian
PY  - 2025/02/25
UR  - https://scipost.org/SciPostPhys.18.2.068
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 2
SP  - 068
A1  - Topchyan, Hrant
AU  - Iugov, Vasilii
AU  - Mirumyan, Mkhitar
AU  - Hakobyan, Tigran S.
AU  - Sedrakyan, Tigran
AU  - Sedrakyan, Ara G.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.2.068,
	title={{Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian}},
	author={Hrant Topchyan and Vasilii Iugov and Mkhitar Mirumyan and Tigran Hakobyan and Tigran A. Sedrakyan and Ara G. Sedrakyan},
	journal={SciPost Phys.},
	volume={18},
	pages={068},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.2.068},
	url={https://scipost.org/10.21468/SciPostPhys.18.2.068},
}