Correlations and enlarged superconducting phase of \(t\)-\(J_\perp\) chains of ultracold molecules on optical lattices

We compute physical properties across the phase diagram of the \(t\)-\(J_\perp\) chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group (DMRG) indicate that superconductivity is enhanced when the Ising component \(J_z\) of the spin-spin interaction and the charge component \(V\) are tuned to zero, and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.