Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The length scale measurements of the Fractional quantum Hall state on
  cylinder   Once the fractional quantum Hall (FQH) state for a finite size system is put
on the surface of a cylinder, the distance between the two ends with open
boundary conditions can be tuned as varying the aspect ratio $\gamma$. It
scales linearly as increasing the system size and therefore has a larger
adjustable range than that on disk. The previous study of the quasi-hole
tunneling amplitude on disk in Ref.~\cite{Zk2011} indicates that the tunneling
amplitudes have a scaling behavior as a function of the tunneling distance and
the scaling exponents are related to the scaling dimension and the charge of
the transported quasiparticles. However, the scaling behaviors poorly due to
the narrow range of the tunneling distance on disk. Here we systematically
study the quasiparticle tunneling amplitudes of the Laughlin state in the
cylinder geometry which shows a much better scaling behavior. Especially, there
are some corssover behaviors at two length scales when the two open edges are
close to each other. These lengths are also reflected in the bipartite
entanglement and the electron Green's function as either a singularity or a
crossover. These two critical length scales of the edge-edge distance,
$L_x^{c_1}$ and $L_x^{c_2}$, are found to be related to the dimension reduction
and back scattering point respectively.

2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg