Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exotic pairing in 1D spin-3/2 atomic gases with $SO(4)$ symmetry   Tuning interactions in the spin singlet and quintet channels of two colliding
atoms could change the symmetry of the one-dimensional spin-3/2 fermionic
systems of ultracold atoms while preserving the integrability. Here we find a
novel $SO(4)$ symmetry integrable point in thespin-3/2 Fermi gas and derive the
exact solution of the model using the Bethe ansatz. In contrast to the model
with $SU(4)$ and $SO(5)$ symmetries, the present model with $SO(4)$ symmetry
preserves spin singlet and quintet Cooper pairs in two sets of $SU(2)\otimes
SU(2)$ spin subspaces. We obtain full phase diagrams, including the
Fulde-Ferrel-Larkin-Ovchinnikov like pair correlations, spin excitations and
quantum criticality through the generalized Yang-Yang thermodynamic equations.
In particular, various correlation functions are calculated by using
finite-size corrections in the frame work of conformal field theory. Moreover,
within the local density approximation, we further find that spin singlet and
quintet pairs form subtle multiple shell structures in density profiles of the
trapped gas.

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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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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: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat