Phase diagram of one-dimensional bosons in an array of local nonlinear potentials at zero temperature

The Gaussian wave functional method is applied to a boson system with an ar ray of local nonlinear potentials cos [beta phi (nR)] to study the phase di agram of its ground state. The stable ground state is determined by the ren ormalized mass mu which is a function of the parameter gamma = beta (2)/4 p i, the strength of potential alpha and the potential concentration c. In di fferent cases gamma < gamma (1), gamma (1) < gamma < gamma (2) and y > gamm a (2), mu can have different multiplicities, the phase diagram in parameter space is thus depicted. The value gamma = gamma (1) depends on the concent ration c, for c --> 0, it coincides with that of the single impurity model; while gamma (2) = 2 coincides with the conclusion of the continuous model.