Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the exact solvability of the anisotropic central spin model: An
  operator approach   Using an operator approach based on a commutator scheme that has been
previously applied to Richardson's reduced BCS model and the inhomogeneous
Dicke model, we obtain general exact solvability requirements for an
anisotropic central spin model with $XXZ$-type hyperfine coupling between the
central spin and the spin bath, without any prior knowledge of integrability of
the model. We outline the basic steps of the usage of the operator approach,
and pedagogically summarize them into two \emph{Lemmas} and two
\emph{Constraints}. Through a step-by-step construction of the eigen-problem,
we show that the condition $g'^2_j-g_j^2=c$ naturally arises for the model to
be exactly solvable, where $c$ is a constant independent of the bath-spin index
$j$, and $\{g_j\}$ and $\{g'_j\}$ are the longitudinal and transverse hyperfine
interactions, respectively. The obtained conditions and the resulting Bethe
ansatz equations are consistent with that in previous literature.

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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci