Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model
  with flat bands   To explore superfluidity in flat-band systems, we consider a Bose-Hubbard
model on a cross-linked ladder with $\pi$ flux, which has a flat band with a
gap between the other band for noninteracting particles, where we study the
effect of the on-site repulsion nonperturbatively. For low densities, we find
exact degenerate ground states, each of which is a Wigner solid with
nonoverlapping Wannier states on the flat band. At higher densities, the
many-body system, when projected onto the lower flat band, can be mapped to a
spin-chain model. This mapping enables us to reveal the existence of a
Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the
high- and low- density regions have an overlap, where the two phases coexist.

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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
2
The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol