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Fumihiko, Sugino
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Novel quantum phases on graphs using abelian gauge theory

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Title
Novel quantum phases on graphs using abelian gauge theory
Author(s)
Pramod Padmanabhan; Fumihiko Sugino
Publication Date
2021-10-01
Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, v.2021, no.10, pp.1 - 44
Publisher
IOP Publishing Ltd
Abstract
© 2021 IOP Publishing Ltd and SISSA Medialab srl Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of an even richer variety than the two-dimensional space. We explore this possibility by building a class of frustration-free and gapped Hamiltonians based on discrete abelian gauge groups. The resulting models have a ground state degeneracy that can be either a topological invariant, an extensive quantity or a mixture of the two. For two basis of the degenerate ground states which are complementary in quantum theory, the entanglement entropy (EE) is exactly computed. The result for one basis has a constant global term, known as the topological EE, implying long-range entanglement. On the other hand, the topological EE vanishes in the result for the other basis. Comparisons are made with similar occurrences in the toric code. We analyze excitations and identify anyon-like excitations that account for the topological EE. An analogy between the ground states of this system and the theta-vacuum for a U(1) gauge theory on a circle is also drawn.
URI
https://pr.ibs.re.kr/handle/8788114/10542
DOI
10.1088/1742-5468/ac25f7
ISSN
1742-5468
Appears in Collections:
Center for Fundamental Theory(순수물리이론 연구단) > 1. Journal Papers (저널논문)
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