Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: d-wave superconductivity in Hubbard model on the square lattice
  perturbed by weak 3D uniaxial anisotropy   The Hubbard model on a square lattice is one of the most studied
condensed-matter quantum problems.Here we find evidence that for intermediate
$U/4t$ values and a hole-concentration range $x\in (x_c,x_*)$ the ground state
of the Hubbard model on the square lattice perturbed by weak three-dimensional
(3D) uniaxial anisotropy has long-range d-wave superconducting order. Here $t$
is the effective nearest-neighbor transfer integral and $U$ the effective
on-site repulsion. The lower critical concentration $x_c$ involves the Ginzburg
number Gi and is approximately given by $x_c\approx {\rm Gi}+x_0\approx 0.05$.
Here $x_0<{\rm Gi}$ is a small critical hole concentration that marks a sharp
quantum phase transition from a Mott-Hubbard insulator with long-range
antiferromagnetic order for $x<x_0$ to an Anderson insulator with short-range
incommensurate spiral spin order for $x\in (x_0,x_c)$. The value of the
critical hole concentration $x_*$ depends on $U/4t$ and is given by $x_*\approx
0.27$ for $U/4t\approx 1.525$. The long-range d-wave superconducting order
emerges below a critical temperature $T_c$ for a hole concentration range
centered at $x_{op}= (x_c+x_*)/2\approx 0.16$. It results from the effects of
the residual interactions of the charge $c$ and spin-neutral two-spinon $s1$
fermions of Ref. \cite{companion2}, as a by-product of the short-range spin
correlations. The spin subsystem provides through such interactions the energy
needed for the effective pairing coupling between the $c$ fermions of the
virtual-electron pair configurations.

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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int