We study the interplay between the long and shortrange interaction of a onedimensional optical
lattice system of twocomponent dipolar fermions by using the density matrix renormalization group
method. The atomic density profile, pairingpairing correlation function, and the compressibility
are calculated in the ground state, from which we identify the parameter region of the FuldeFerrellLarkinOvchinnikov
(FFLO) pairing state, halfmetal (HM) state, FFLOHM state, and the
normal polarized state, and thus the phase diagram in the coordinates of the long and shortrange
interaction strength. The effect of the longrange dipolar interaction on the FFLO state is discussed
in details. We find that the longrange part of the dipoledipole interaction does not sweep away
the FFLO superconducting region that is driven by the shortrange interaction in the Hubbard
model, and thus the FFLO state survives in the wide parameter space of the longrange interaction,
polarization and the filling.
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