Quantum phase diagrams of fermionic dipolar gases in a planar array of one-dimensional tubes

We systematically study ground-state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized Bogoliubov transformation, we calculate the elementary excitations and the Luttinger scaling exponents for various relevant quantum orders. The complete quantum phase diagrams for arbitrary polar angle of the dipole moment are obtained including charge-density wave, p-wave superfluid, intertube gauge-phase density wave, and intertube s-wave superfluid, where the last two break the U(1) gauge symmetry of the system (conservation of particle number in each tube) and occur only when the intertube interaction is larger than the intratube interaction. We then discuss the physical properties and experimental features of these many-body phases.