Lemm, Marius2020-10-012020-10-012020-10-01202010.1090/conm/741/14923https://infoscience.epfl.ch/handle/20.500.14299/172122We generalize the existing finite-size criteria for spectral gaps offrustration-free spin systems to D>2 dimensions. We obtain a local gapthreshold of 3/n, independent of D, for nearest-neighbor interactions. The 1/n scaling persists for arbitrary finite-range interactions in Z3. The key observation is that there is more flexibility in Knabe’s combinatorial approach if one employs the operator Cauchy-Schwarz inequality.text::book/monograph::book part or chapter