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The extended Bose-Hubbard model in a quadratic trap potential is studiedusing a finite-size density-matrix renormalization group method (DMRG). Wecompute the boson density profiles, the local compressibility and the hoppingcorrelation functions. We observed the phase separation induced by the trap inall the quantities studied and conclude that the local density approximation isvalid in the extended Bose-Hubbard model. From the plateaus obtained in thelocal compressibility it was possible to obtain the phase diagram of thehomogeneous system which is in agreement with previous results.Comment: 14 pages, 11 figure

One-dimensional extended Bose–Hubbard model with a confining potential: a DMRG analysis