  The nature of the low energy spectrum of frustrated quantum spin systems is
investigated by means of a topological test introduced by Y. Hatsugai which
enables to infer the possible existence or absence of a gap between the ground
state and excited states of these systems. The test relies on the determination
of an order parameter which is a Berry phase. The structure of the spectra of
even and odd-legged systems in 2d and 3d is analyzed. Results are confronted
with previous work.
