The Berry phase: a topological test for the spectrum structure of frustrated quantum spin systems

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.