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

Fuente: arXiv
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Auteurs principaux: Topchyan, Hrant, Iugov, Vasilii, Mirumyan, Mkhitar, Hakobyan, Tigran S., Sedrakyan, Tigran A., Sedrakyan, Ara G.
Format: Preprint
Publié: 2023
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author Topchyan, Hrant
Iugov, Vasilii
Mirumyan, Mkhitar
Hakobyan, Tigran S.
Sedrakyan, Tigran A.
Sedrakyan, Ara G.
author_facet Topchyan, Hrant
Iugov, Vasilii
Mirumyan, Mkhitar
Hakobyan, Tigran S.
Sedrakyan, Tigran A.
Sedrakyan, Ara G.
contents 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 Preprint
id arxiv_https___arxiv_org_abs_2312_15095
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian
Topchyan, Hrant
Iugov, Vasilii
Mirumyan, Mkhitar
Hakobyan, Tigran S.
Sedrakyan, Tigran A.
Sedrakyan, Ara G.
Strongly Correlated Electrons
Statistical Mechanics
High Energy Physics - Theory
Quantum Physics
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.
title Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian
topic Strongly Correlated Electrons
Statistical Mechanics
High Energy Physics - Theory
Quantum Physics
url https://arxiv.org/abs/2312.15095