Two-dimensional topological paramagnets protected by \(\mathbb{Z}_3\) symmetry: Properties of the boundary Hamiltonian

We systematically construct two-dimensional \(\mathbb{Z}_3\) symmetry-protected topological (SPT) three-state Potts paramagnets with gapless edge modes on a triangular lattice. First, we study microscopic lattice models for the gapless edge and, using the density-matrix renormalization group (DMRG)...

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Published inarXiv.org
Main Authors Topchyan, Hrant, Iugov, Vasilii, Mirumyan, Mkhitar, Hakobyan, Tigran S, Sedrakyan, Tigran A, Sedrakyan, Ara G
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.12.2023
Subjects
Entanglement
Excitation spectra
Field theory
Lattice vibration
Symmetry
Topology
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Summary:We systematically construct two-dimensional \(\mathbb{Z}_3\) symmetry-protected topological (SPT) three-state Potts paramagnets with gapless edge modes on a triangular lattice. First, we study 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 SPT phases. As a result, the two topologically nontrivial and the trivial phases define a general one-dimensional chain supporting a tricriticality, which we argue supports a gapless SPT order in one dimension.
ISSN:2331-8422