1D quasicrystals and topological markers
Author(s)
Sykes, Joseph
Barnett, Ryan
Type
Journal Article
Abstract
Local topological markers are effective tools for determining the topological properties of both
homogeneous and inhomogeneous systems. The Chern marker is an established topological
marker that has previously been shown to effectively reveal the topological properties of 2D
systems. In an earlier work, the present authors have developed a marker that can be applied to 1D
time-dependent systems which can be used to explore their topological properties, like charge
pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that
it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against
different quasicrystal Hamiltonians, some which have been addressed in previous studies using
existing methods, and others which possess topological structures that have been largely
unexplored. We also demonstrate that the altered 1D marker can be productively applied to
systems that are fully aperiodic.
homogeneous and inhomogeneous systems. The Chern marker is an established topological
marker that has previously been shown to effectively reveal the topological properties of 2D
systems. In an earlier work, the present authors have developed a marker that can be applied to 1D
time-dependent systems which can be used to explore their topological properties, like charge
pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that
it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against
different quasicrystal Hamiltonians, some which have been addressed in previous studies using
existing methods, and others which possess topological structures that have been largely
unexplored. We also demonstrate that the altered 1D marker can be productively applied to
systems that are fully aperiodic.
Date Issued
2022-06-01
Date Acceptance
2022-06-01
Citation
Materials for Quantum Technology, 2022, 2 (2), pp.025005-025005
ISSN
2633-4356
Publisher
IOP Publishing
Start Page
025005
End Page
025005
Journal / Book Title
Materials for Quantum Technology
Volume
2
Issue
2
Copyright Statement
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citation and DOI.
this work may be used
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maintain attribution to
the author(s) and the
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citation and DOI.
License URL
Identifier
https://iopscience.iop.org/article/10.1088/2633-4356/ac75a6
Subjects
cond-mat.quant-gas
cond-mat.quant-gas
cond-mat.mtrl-sci
quant-ph
Publication Status
Published
Date Publish Online
2022-06-20