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We systematically study ground state properties of fermionic dipolar gases ina planar array of one-dimensional potential tubes for an arbitrary orientationof dipole moments. Using the Luttinger liquid theory with the generalizedBogoliubov transformation, we calculate the elementary excitations and theLuttinger scaling exponents for various relevant quantum orders. The completequantum phase diagrams for arbitrary polar angle of the dipole moment isobtained, including charge density wave, p-wave superfluid, inter-tubegauge-phase density wave, and inter-tube s-wave superfluid, where the last twobreaks the U(1) gauge symmetry of the system (conservation of particle numberin each tube) and occurs only when the inter-tube interaction is larger thanthe intra-tube interaction. We then discuss the physical properties of thesemany-body phases and their relationship with some solid state systems.

Quantum phase diagrams of fermionic dipolar gases for an arbitrary orientation of dipole moment in a planar array of 1D tubes