Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nambu-Eliashberg theory for multi-scale quantum criticality :
  Application to ferromagnetic quantum criticality in the surface of three
  dimensional topological insulators   We develop an Eliashberg theory for multi-scale quantum criticality,
considering ferromagnetic quantum criticality in the surface of three
dimensional topological insulators. Although an analysis based on the random
phase approximation has been performed for multi-scale quantum criticality, an
extension to an Eliashberg framework was claimed to be far from triviality in
respect that the self-energy correction beyond the random phase approximation,
which originates from scattering with $z = 3$ longitudinal fluctuations,
changes the dynamical exponent $z = 2$ in the transverse mode, explicitly
demonstrated in nematic quantum criticality. A novel ingredient of the present
study is to introduce an anomalous self-energy associated with the spin-flip
channel. Such an anomalous self-energy turns out to be essential for
self-consistency of the Eliashberg framework in the multi-scale quantum
critical point because this off diagonal self-energy cancels the normal
self-energy exactly in the low energy limit, preserving the dynamics of both $z
= 3$ longitudinal and $z = 2$ transverse modes. This multi-scale quantum
criticality is consistent with that in a perturbative analysis for the nematic
quantum critical point, where a vertex correction in the fermion bubble diagram
cancels a singular contribution due to the self-energy correction, maintaining
the $z = 2$ transverse mode. We also claim that this off diagonal self-energy
gives rise to an artificial electric field in the energy-momentum space in
addition to the Berry curvature. We discuss the role of such an anomalous
self-energy in the anomalous Hall conductivity.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int