Superfluid-Mott insulator and superfluid-charge density wave transitions in a one-dimensional Bose–Hubbard model

The superfluid to the Mott insulator transition is studied in the Bose–Hubbard model with contact interactions U at the density ρ=1, and at the half-filling ρ=1/2 added the next nearest interactions V which is responsible for the charge density wave (CDW). The Berezinski–Kosterlitz–Thouless transition is analyzed from the points of the dual Sine–Gordon model and the boson-spin equivalence by the conformal field theory. Eventually the prescription for the boson system is developed and the Mott insulator transition point and the superfluid to CDW transition point are estimated.