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Subsystem Ginzburg-Landau and symmetry-protected topological order coexisting on a graph

Authors
Kim, JintaeLee, Hyun-YongHan, Jung Hoon
Issue Date
12-5월-2021
Publisher
AMER PHYSICAL SOC
Citation
PHYSICAL REVIEW B, v.103, no.19
Indexed
SCIE
SCOPUS
Journal Title
PHYSICAL REVIEW B
Volume
103
Number
19
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/128037
DOI
10.1103/PhysRevB.103.195124
ISSN
2469-9950
Abstract
We write down and analyze a model demonstrating the co-existence of conventional symmetry-breaking order and symmetry-protected topological (SPT) order in the one-dimensional chain. When appropriately generalized to a model on a graph, the SPT and symmetry-breaking orders exist for each individual loop, or cycle, of the graph. It arises as a consequence of the kind of "global" symmetry operator responsible for SPT and the local-order parameter defining the Ginzburg-Landau order, both of which exist in our model and commute with the Hamiltonian. The anti-commuting character of these two-order parameters is responsible for the ground state degeneracy (GSD). As such operators and their anti-commuting relations can be defined for each independent loop, the GSD grows exponentially with the first Betti number for a graph.
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