Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Macroscopic quantum spin tunnelling with two interacting spins   We study the simple Hamiltonian, $H=-K(S_{1z}^2 +S_{2z}^2)+ \lambda\vec
S_1\cdot\vec S_2$, of two, large, coupled spins which are taken equal, each of
total spin $s$ with $\lambda$ the exchange coupling constant. The exact ground
state of this simple Hamiltonian is not known for an antiferromagnetic coupling
corresponding to the $\lambda>0$. In the absence of the exchange interaction,
the ground state is four fold degenerate, corresponding to the states where the
individual spins are in their highest weight or lowest weight states,
$|\hskip-1 mm\uparrow, \uparrow\rangle, |\hskip-1 mm\downarrow,
\downarrow\rangle, |\hskip-1 mm\uparrow, \downarrow\rangle, |\hskip-1
mm\downarrow, \uparrow\rangle$, in obvious notation. The first two remain exact
eigenstates of the full Hamiltonian. However, we show the that the two states $
|\hskip-1 mm\uparrow, \downarrow\rangle, |\hskip-1 mm\downarrow,
\uparrow\rangle$ organize themselves into the combinations
$|\pm\rangle=\frac{1}{\sqrt 2} (|\hskip-1 mm\uparrow, \downarrow\rangle \pm
|\hskip-1 mm\downarrow \uparrow\rangle)$, up to perturbative corrections. For
the anti-ferromagnetic case, we show that the ground state is non-degenerate,
and we find the interesting result that for integer spins the ground state is
$|+\rangle$, and the first excited state is the anti-symmetric combination
$|-\rangle$ while for half odd integer spin, these roles are exactly reversed.
The energy splitting however, is proportional to $\lambda^{2s}$, as expected by
perturbation theory to the $2s^{\rm th}$ order. We obtain these results through
the spin coherent state path integral.

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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org