Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonperturbative functional renormalization-group approach to transport
  in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical
  point   Using a nonperturbative functional renormalization-group approach to the
two-dimensional quantum O($N$) model, we compute the low-frequency limit
$\omega\to 0$ of the zero-temperature conductivity in the vicinity of the
quantum critical point. Our results are obtained from a derivative expansion to
second order of a scale-dependent effective action in the presence of an
external (i.e., non-dynamical) non-Abelian gauge field. While in the disordered
phase the conductivity tensor $\sigma(\omega)$ is diagonal, in the ordered
phase it is defined, when $N\geq 3$, by two independent elements, $\sigma_{\rm
A}(\omega)$ and $\sigma_{\rm B}(\omega)$, respectively associated to SO($N$)
rotations which do and do not change the direction of the order parameter. For
$N=2$, the conductivity in the ordered phase reduces to a single component
$\sigma_{\rm A}(\omega)$. We show that $\lim_{\omega\to
0}\sigma(\omega,\delta)\sigma_{\rm A}(\omega,-\delta)/\sigma_q^2$ is a
universal number which we compute as a function of $N$ ($\delta$ measures the
distance to the quantum critical point, $q$ is the charge and $\sigma_q=q^2/h$
the quantum of conductance). On the other hand we argue that the ratio
$\sigma_{\rm B}(\omega\to 0)/\sigma_q$ is universal in the whole ordered phase,
independent of $N$ and, when $N\to\infty$, equal to the universal conductivity
$\sigma^*/\sigma_q$ at the quantum critical point.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph