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We use Abelian Bosonization and density matrix renormalization group methodto study the effect of density on quantum phases of long range 1-D Bose-Hubbardmodel. We predict the existence of supersolid phase and also other quantumphases for this system. We have analyzed the role of long range interactionparameter on solitonic phase near half filling. We discuss the effect ofdimerization in nearest neighbor hopping and interaction terms on the plateauphase at the half filling.

Quantum Phases of Long Range 1-D Bose-Hubbard Model: Field Theoretic and DMRG Study at Different Densities