  We show that ultracold two-component fermionic dipolar gases in an optical
lattice with strong two-body on-site loss can be used to realize a tunable
effective spin-one model. Fermion number conservation provides an unusual
constraint that $\sum_i (S^z_i)^2$ is conserved, leading to a novel topological
liquid phase in one dimension which can be thought of as the gapless analog of
the Haldane gapped phase of a spin-one Heisenberg chain. The properties of this
phase are calculated numerically via the infinite time-evolving block
decimation method and analytically via a mapping to a one-mode Luttinger liquid
with hidden spin information.
