  We study the excitation spectrum of a family of transverse-field spin chain
models with variable interaction range and arbitrary spin $S$, which in the
case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising
model. For any finite number $N$ of spins, a semiclassical energy manifold is
derived in the large-$S$ limit employing bosonization methods, and its geometry
is shown to determine not only the leading-order term but also the higher-order
quantum fluctuations. Based on a multi-configurational mean-field ansatz, we
obtain the semiclassical backbone of the quantum spectrum through the extremal
points of a series of one-dimensional energy landscapes -- each one exhibiting
a bifurcation when the external magnetic field drops below a threshold value.
The obtained spectra become exact in the limit of vanishing or very strong
external, transverse magnetic fields. Further analysis of the higher-order
corrections in $1/\sqrt{2S}$ enables us to analytically study the dispersion
relations of spin-wave excitations around the semiclassical energy levels.
Within the same model, we are able to investigate quantum bifurcations, which
occur in the semiclassical ($S\gg 1$) limit, and quantum phase transitions,
which are observed in the thermodynamic ($N\rightarrow\infty$) limit.
