Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solution of the two-axis countertwisting Hamiltonian   It is shown that the two-axis countertwisting Hamiltonian is exactly solvable
when the quantum number of the total angular momentum of the system is an
integer after the Jordan-Schwinger (differential) boson realization of the
SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with
the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz
equations of the problem is derived. It is shown that solutions of the Bethe
ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials.
The total number of the four sets of the zeros equals exactly to $2J+1$ for a
given integer angular momentum quantum number $J$, which proves the
completeness of the solutions. It is also shown that double degeneracy in level
energies may also occur in the $J\rightarrow\infty$ limit for integer $J$ case
except a unique non-degenerate level with zero excitation energy.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
19
The categories of this paper are: eess
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg