Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability of the $\nu=4/3$ fractional quantum Hall edge states   We investigate the homogeneous chiral edge theory of the filling $\nu=4/3$
fractional quantum Hall state, which is parameterized by a Luttinger liquid
velocity matrix and an electron tunneling amplitude (ignoring irrelevant
terms). We identify two solvable cases: one case where the theory gives two
free chiral boson modes, and the other case where the theory yields one free
charge $\frac{2e}{\sqrt{3}}$ chiral fermion and two free chiral Bogoliubov
(Majorana) fermions. For generic parameters, the energy spectrum from our exact
diagonalization shows Poisson level spacing statistics (LSS) in each conserved
charge and momentum sector, indicating the existence of hidden conserved
quantities and the possibility that the generic edge theory of the $\nu=4/3$
fractional quantum Hall state is integrable. We further show that a global
symmetry preserving irrelevant nonlinear kinetic term will lead to the
transition of LSS from Poisson to Wigner-Dyson at high energies. This further
supports the possibility that the model without irrelevant terms is integrable.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex