  We examine solitons in theories with heavy fermions. These ``quantum''
solitons differ dramatically from semi-classical (perturbative) solitons
because fermion loop effects are important when the Yukawa coupling is strong.
We focus on kinks in a $(1+1)$--dimensional $\phi^4$ theory coupled to
fermions; a large-$N$ expansion is employed to treat the Yukawa coupling $g$
nonperturbatively. A local expression for the fermion vacuum energy is derived
using the WKB approximation for the Dirac eigenvalues. We find that fermion
loop corrections increase the energy of the kink and (for large $g$) decrease
its size. For large $g$, the energy of the quantum kink is proportional to $g$,
and its size scales as $1/g$, unlike the classical kink; we argue that these
features are generic to quantum solitons in theories with strong Yukawa
couplings. We also discuss the possible instability of fermions to solitons.
