Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many-body perturbation theory for the superconducting quantum dot:
  Fundamental role of the magnetic field   We develop the general many-body perturbation theory for a superconducting
quantum dot represented by a single-impurity Anderson model attached to
superconducting leads. We build our approach on a thermodynamically consistent
mean-field approximation with a two-particle self-consistency of the parquet
type. The two-particle self-consistency leading to a screening of the bare
interaction proves substantial for suppressing the spurious transitions of the
Hartree-Fock solution. We demonstrate that the magnetic field plays a
fundamental role in the extension of the perturbation theory beyond the weakly
correlated $0$-phase. It controls the critical behavior of the $0-\pi$ quantum
transition, lifts the degeneracy in the $\pi$-phase, where the limits to zero
temperature and zero magnetic field do not commute. The response to the
magnetic field is quite different in $0$- and $\pi$-phases. While the magnetic
susceptibility vanishes in the $0$-phase it becomes of the Curie type and
diverges in the $\pi$-phase at zero temperature.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex