  In quantum many-body systems, the existence of a spectral gap above the
ground state has far-reaching consequences. In this paper, we discuss
"finite-size" criteria for having a spectral gap in frustration-free spin
systems and their applications. We extend a criterion that was originally
developed for periodic systems by Knabe and Gosset-Mozgunov to systems with a
boundary. Our finite-size criterion says that if the spectral gaps at linear
system size $n$ exceed an explicit threshold of order $n^{-3/2}$, then the
whole system is gapped. The criterion takes into account both "bulk gaps" and
"edge gaps" of the finite system in a precise way. The $n^{-3/2}$ scaling is
robust: it holds in 1D and 2D systems, on arbitrary lattices and with arbitrary
finite-range interactions. One application of our results is to give a rigorous
foundation to the folklore that 2D frustration-free models cannot host chiral
edge modes (whose finite-size spectral gap would scale like $n^{-1}$).
