The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice

TL;DR

This paper predicts a new gapless topological phase called the 'Haldane Liquid' in a one-dimensional cold polar molecular lattice, realized through ultracold fermionic gases with strong on-site loss, combining numerical and analytical methods.

Contribution

It introduces a novel gapless topological phase in a one-dimensional system, expanding the understanding of topological states in cold atom setups.

Findings

Identification of a gapless topological phase analogous to the Haldane phase.

Numerical confirmation using infinite time-evolving block decimation.

Analytical mapping to a Luttinger liquid with hidden spin information.

Abstract

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.