Loops, sign structures and emergent Fermi statistics in three-dimensional quantum dimer models

We introduce and study three-dimensional quantum dimer models with positive resonance terms. We demonstrate that their ground state wavefunctions exhibit a nonlocal sign structure that can be exactly formulated in terms of loops, and as a direct consequence, monomer excitations obey Fermi statistics. The sign structure and Fermi statistics in these ``signful'' quantum dimer models can be naturally described by a novel parton construction, which becomes exact at the solvable point.