2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165124The 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.11 pages, 1 figureStrongly Correlated Electronstext