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Two-dimensional topological paramagnets protected by $Z_3$ symmetry: Properties of the boundary Hamiltonian

by Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan, Tigran S. Hakobyan, Tigran A. Sedrakyan, Ara G. Sedrakyan

Submission summary

Authors (as registered SciPost users):

Vasilii Iugov · Tigran Sedrakyan

Abstract

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 symmetry distinguishing between two possible $\mathbb{Z}_3$ SPT phases. As a result, the two topologically non-trivial and one trivial phases define a general one-dimensional chain supporting a tricriticality, which we argue supports a gapless SPT order in one dimension. 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.