Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly correlated superconductivity   Band theory and BCS theory are arguably the most successful theories of
condensed matter physics. Yet, in a number of materials, in particular the
high-temperature superconductors and the layered organic superconductors, they
fail. In these lecture notes for an international school, I emphasize that even
though the low energy properties of a phase of matter are generally emergent
and entirely determined by the broken symmetry, there are many differences
between a strongly correlated and a weakly correlated state of matter. For
example, spin waves are an emergent property for antiferromagnets, but for weak
correlations the normal phase of a (Slater) antiferromagnet is metallic,
whereas it is insulating (Heisenberg) for strong correlations. As a function of
interaction strength, above the antiferromagnetic phase, the crossover between
a metal and a local moment paramagnetic insulator is described by the Mott
transition, whose mean-field theory down to T=0 is best formulated with
dynamical mean-field theory. A similar situation occurs for superconductors:
despite similar emergent properties, there are many differences between both
kinds of superconductors. Experimental evidence suggests that hole-doped
cuprates are strongly correlated whereas the correlations are weaker in the
electron-doped case, especially near optimal doping. Evidence for a pseudogap
arising from antiferromagnetic fluctuations is strong in the latter case,
whereas in the hole-doped case the pseudogap temperature appears as a
consequence of Mott physics. In cluster dynamical mean-field theory, the
pseudogap line T* is a Widom line arising from a T=0 first-order transition
that terminates at a finite T critical point. Strongly correlated
superconductors are much more resilient to near-neighbor repulsion than their
weakly correlated counterpart. Many different methods to attack these problems
theoretically are described.

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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph