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We study the interplay between the long- and short-range interaction of a one-dimensional optical
lattice system of two-component dipolar fermions by using the density matrix renormalization group
method. The atomic density profile, pairing-pairing correlation function, and the compressibility
are calculated in the ground state, from which we identify the parameter region of the FuldeFerrell-Larkin-Ovchinnikov
(FFLO) pairing state, half-metal (HM) state, FFLO-HM state, and the
normal polarized state, and thus the phase diagram in the coordinates of the long- and short-range
interaction strength. The effect of the long-range dipolar interaction on the FFLO state is discussed
in details. We find that the long-range part of the dipole-dipole interaction does not sweep away
the FFLO superconducting region that is driven by the short-range interaction in the Hubbard
model, and thus the FFLO state survives in the wide parameter space of the long-range interaction,
polarization and the filling.
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