We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64\times 64$ square lattice we demonstrate the existence of a novel phase, possessing an “ultralong-range” order. The fingerprint of this phase—the density correlation function—features a nontrivial behavior on a scale of tens of lattice sites. We study the properties and the stability of the ultralong-range-ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms.

• Received 19 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.081106