Nonzero spectral gap in several uniformly spin-2 and hybrid spin-1 and spin-2 AKLT models

Quantitatively improved finite-size criteria for spectral gaps

“…Most importantly, finite-size criteria have been used to derive spectral gaps in several concrete physical Hamiltonians of relevance. Examples where finite-size played an important role include AKLT-type models [1,9,20,21,26,27], Haldane pseudopotential models for the fractional quantum hall effect [24,29,30], randomly generated translation-invariant Hamiltonians [14][15][16], product vacua with boundary states Hamiltonians [19], various frustration-free Hamiltonians generated by Witten's conjugation [33], and unitary k-designs in quantum information theory [10]. The existence of a spectral gap is important to pin down precisely the quantum phase exhibited by the ground state.…”