Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple $\mathbb{Z}_2$ lattice gauge theories at finite fermion density   Lattice gauge theories are a powerful language to theoretically describe a
variety of strongly correlated systems, including frustrated magnets,
high-$T_c$ superconductors, and topological phases. However, in many cases
gauge fields couple to gapless matter degrees of freedom and such theories
become notoriously difficult to analyze quantitatively. In this paper we study
several examples of $\mathbb{Z}_2$ lattice gauge theories with gapless fermions
at finite density, in one and two spatial dimensions, that are either exactly
soluble or whose solution reduces to that of a known problem. We consider
complex fermions (spinless and spinful) as well as Majorana fermions, and study
both theories where Gauss' law is strictly imposed and those where all
background charge sectors are kept in the physical Hilbert space. We use a
combination of duality mappings and the $\mathbb{Z}_2$ slave-spin
representation to map our gauge theories to models of gauge-invariant fermions
that are either free, or with on-site interactions of the Hubbard or
Falicov-Kimball type that are amenable to further analysis. In 1D, the phase
diagrams of these theories include free-fermion metals, insulators, and
superconductors; Luttinger liquids; and correlated insulators. In 2D, we find a
variety of gapped and gapless phases, the latter including uniform and
spatially modulated flux phases featuring emergent Dirac fermions, some
violating Luttinger's theorem.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga