Dynamic properties of the one-dimensional Bose-Hubbard model

Abstract

We use the density-matrix renormalization group method to investigate\nground-state and dynamic properties of the one-dimensional Bose-Hubbard model,\nthe effective model of ultracold bosonic atoms in an optical lattice. For fixed\nmaximum site occupancy $n_b=5$, we calculate the phase boundaries between the\nMott insulator and the `superfluid' phase for the lowest two Mott lobes. We\nextract the Tomonaga-Luttinger parameter from the density-density correlation\nfunction and determine accurately the critical interaction strength for the\nMott transition. For both phases, we study the momentum distribution function\nin the homogeneous system, and the particle distribution and quasi-momentum\ndistribution functions in a parabolic trap. With our zero-temperature method we\ndetermine the photoemission spectra in the Mott insulator and in the\n`superfluid' phase of the one-dimensional Bose-Hubbard model. In the insulator,\nthe Mott gap separates the quasi-particle and quasi-hole dispersions. In the\n`superfluid' phase the spectral weight is concentrated around zero momentum.\n