Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hofstadter Butterfly Evolution in the Space of Two-Dimensional Bravais
  Lattices   The self-similar energy spectrum of a particle in a periodic potential under
a magnetic field, known as the Hofstadter butterfly, is determined by the
lattice geometry as well as the external field. Recent realizations of
artificial gauge fields and adjustable optical lattices in cold atom
experiments necessitate the consideration of these self-similar spectra for the
most general two-dimensional lattice. In a previous work, we investigated the
evolution of the spectrum for an experimentally realized lattice which was
tuned by changing the unit cell structure but keeping the square Bravais
lattice fixed. We now consider all possible Bravais lattices in two dimensions
and investigate the structure of the Hofstadter butterfly as the lattice is
deformed between lattices with different point symmetry groups. We model the
optical lattice by a sinusoidal real space potential and obtain the tight
binding model for any lattice geometry by calculating the Wannier functions. We
introduce the magnetic field via Peierls substitution and numerically calculate
the energy spectrum. The transition between the two most symmetric lattices,
i.e. the triangular and the square lattice displays the importance of bipartite
symmetry featuring deformation as well as closing of some of the major energy
gaps. The transition from the square to rectangular and from the triangular to
centered rectangular lattices are analyzed in terms of coupling of
one-dimensional chains. We calculate the Chern numbers of the major gaps and
Chern number transfer between bands during the transitions. We use gap Chern
numbers to identify distinct topological regions in the space of Bravais
lattices.

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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cs