  Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ
spin model and feature $n$ particle species on $\mathbb Z^d$. The PVBS models
were originally introduced as toy models for the classification of ground state
phases. A crucial ingredient for this classification is the existence of a
spectral gap above the ground state sector. In this work, we derive a spectral
gap for PVBS models at arbitrary species number $n$ and in arbitrary dimension
$d$ in the perturbative regime of small anisotropy parameters. Instead of using
the more common martingale method, the proof verifies a finite-size criterion
in the spirit of Knabe.
