  In this paper we investigate an integrable loop model and its connection with
a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some
properties of the ground state. When the loop fugacity $q$ lies in the physical
regime, we conjecture that the central charge is $c=q-1$ for $q$ integer $< 2$.
Low-lying excitations are examined, supporting a superdiffusive behavior for
$q=1$. We argue that these systems are interesting examples of integrable
lattice models realizing $c \leq 0$ conformal field theories.
