  Long lived quasi-stationary states (QSSs) are a signature characteristic of
long-range interacting systems both in the classical and in the quantum realms.
Often, they emerge after a sudden quench of the Hamiltonian internal parameters
and present a macroscopic life-time, which increases with the system size.
Despite their ubiquity, the fundamental mechanism at their root remains
unknown. Here, we show that the spectrum of systems with power-law decaying
couplings remains discrete up to the thermodynamic limit. As a consequence,
several traditional results on the chaotic nature of the spectrum in many-body
quantum systems are not satisfied in presence of long-range interactions. In
particular, the existence of QSSs may be traced back to the finiteness of
Poincar\'e recurrence times. This picture justifies and extends known results
on the anomalous magnetization dynamics in the quantum Ising model with
power-law decaying couplings. The comparison between the discrete spectrum of
long-range systems and more conventional examples of pure point spectra in the
disordered case is also discussed.
