Prediction of a gapless topological Haldane liquid phase in a one-dimensional cold polar molecular lattice

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 Sigma(i)(S(i)(z))(2) is conserved, leading to a unique 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.