Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher
  Genus Surface   We explore the hyperbolic band theory under a magnetic field for the first
time. Our theory is a general extension of the conventional band theory defined
on a Euclidean lattice into the band theory on a general hyperbolic
lattice/Riemann surface. Our methods and results can be confirmed
experimentally by circuit quantum electrodynamics (cQED), which enables us to
create novel materials in a hyperbolic space. To investigate the band
structures, we construct directly the hyperbolic magnetic Bloch states and find
that they form Dirac cones on a coordinate neighborhood, by which they can be
regarded as a global quantum gravity solution detectable in a laboratory.
Besides this is the first explicit example of a massless Dirac state on a
higher genus surface. Moreover we show that the energy spectrum exhibits an
unusual fractal structure refracting the negative curvature, when plotted as a
function of a magnetic flux.

34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci