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 ${\sum }_i(S_i^z){}^2$ 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 Lüttinger liquid with hidden spin information.

• Received 17 March 2011

DOI:https://doi.org/10.1103/PhysRevB.83.174409