Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chiral spin liquids with crystalline $\mathbb{Z}_2$ gauge order in a
  three-dimensional Kitaev model   Chiral spin liquids (CSLs) are time-reversal symmetry breaking ground states
of frustrated quantum magnets that show no long-range magnetic ordering, but
instead exhibit topological order and fractional excitations. Their realization
in simple and tractable microscopic models has, however, remained an open
challenge for almost two decades until it was realized that Kitaev models on
lattices with odd-length loops are natural hosts for such states, even in the
absence of a time-reversal symmetry breaking magnetic field. Here we report on
the formation of CSLs in a three-dimensional Kitaev model, which differ from
their widely studied two-dimensional counterparts, namely, they exhibit a
crystalline ordering of the $\mathbb{Z}_2$ gauge fluxes and thereby break some
of the underlying lattice symmetries. We study the formation of these
unconventional CSLs via extensive quantum Monte Carlo simulations and
demonstrate that they are separated from the featureless paramagnet at high
temperatures by a single first-order transition at which both time-reversal and
lattice symmetries are simultaneously broken. Using variational approaches for
the ground state, we explore the effect of varying the Kitaev couplings and
find at least five distinct CSL phases, all of which possess crystalline
ordering of the $\mathbb{Z}_2$ gauge fluxes. For some of these phases, the
complementary itinerant Majorana fermions exhibit gapless band structures with
topological features such as Weyl nodes or nodal lines in the bulk and Fermi
arc or drumhead surface states.

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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th