Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional Renormalization Group for multi-orbital Fermi Surface
  Instabilities   Technological progress in material synthesis, as well as artificial
realization of condensed matter scenarios via ultra-cold atomic gases in
optical lattices or epitaxial growth of thin films, is opening the gate to
investigate a plethora of unprecedented strongly correlated electron systems.
In a large subclass thereof, a metallic state of layered electrons undergoes an
ordering transition below some temperature into unconventional states of matter
driven by electronic correlations, such as magnetism, superconductivity, or
other Fermi surface instabilities. While this type of phenomena has been a
well-established direction of research in condensed matter for decades, the
variety of today's accessible scenarios pose fundamental new challenges to
describe them. A core complication is the multi-orbital nature of the
low-energy electronic structure of these systems, such as the multi-d orbital
nature of electrons in iron pnictides and transition-metal oxides in general,
but also electronic states of matter on lattices with multiple sites per unit
cell such as the honeycomb or kagome lattice. In this review, we propagate the
functional renormalization group (FRG) as a suited approach to investigate
multi-orbital Fermi surface instabilities. The primary goal of the review is to
describe the FRG in explicit detail and render it accessible to everyone both
at a technical and intuitive level. Summarizing recent progress in the field of
multi-orbital Fermi surface instabilities, we illustrate how the unbiased
fashion by which the FRG treats all kinds of ordering tendencies guarantees an
adequate description of electronic phase diagrams and often allows to obtain
parameter trends of sufficient accuracy to make qualitative predictions for
experiments. This review includes detailed and illustrative illustrations of
magnetism and, in particular, superconductivity for the iron pnictides from the
viewpoint of FRG. Furthermore, it discusses candidate scenarios for topological
bulk singlet superconductivity and exotic particle-hole condensates on
hexagonal lattices such as sodium-doped cobaltates, graphene doped to van Hove
Filling, and the kagome Hubbard model. In total, the FRG promises to be one of
the most versatile and revealing numerical approaches to address unconventional
Fermi surface instabilities in future fields of condensed matter research.

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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: q-alg