Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological models in rotationally symmetric quasicrystals   We investigate the physics of quasicrystalline models in the presence of a
uniform magnetic field, focusing on the presence and construction of
topological states. This is done by using the Hofstadter model but with the
sites and couplings denoted by the vertex model of the quasicrystal, giving the
Hofstadter vertex model. We specifically consider two-dimensional quasicrystals
made from tilings of two tiles with incommensurate areas, focusing on the
five-fold Penrose and the eight-fold Ammann-Beenker tilings. This introduces
two competing scales; the uniform magnetic field and the incommensurate scale
of the cells of the tiling. Due to these competing scales the periodicity of
the Hofstadter butterfly is destroyed. We observe the presence of topological
edge states on the boundary of the system via the Bott index that exhibit two
way transport along the edge. For the eight-fold tiling we also observe
internal edge-like states with non-zero Bott index, which exhibit two way
transport along this internal edge. The presence of these internal edge states
is a new characteristic of quasicrystalline models in magnetic fields. We then
move on to considering interacting systems. This is challenging, in part
because exact diagonalization on a few tens of sites is not expected to be
enough to accurately capture the physics of the quasicrystalline system, and in
part because it is not clear how to construct topological flatbands having a
large number of states. We show that these problems can be circumvented by
building the models analytically, and in this way we construct models with
Laughlin type fractional quantum Hall ground states.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
2
The categories of this paper are: math
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex