  In this paper, we present the exact solution to a one-dimensional,
two-component, quantum many-body system in which like particles interact with a
pair potential $s(s+1)/{\rm sinh}^{2}(r)$, while unlike particles interact with
a pair potential $-s(s+1)/{\rm cosh}^{2}(r)$. We first give a proof of
integrability, then derive the coupled equations determining the complete
spectrum. All singularities occur in the ground state when there are equal
numbers of the two components; we give explicit results for the ground state
and low-lying states in this case. For $s>0$, the system is an
antiferromagnet/insulator, with excitations consisting of a pair-hole--pair
continuum, a two-particle continuum with gap, and excitons with gaps. For
$-1<s<0$, the system has excitations consisting of a hole-particle continuum,
and a two-spin wave continuum, both gap-less.
