Low-energy effective theory for one-dimensional lattice bosons near integer filling

A low-energy effective theory for interacting bosons on a one-dimensional lattice at and near integer fillings is proposed. It is found that two sets of bosonic phase fields are necessary in order to explain the complete phase diagram. Using the present effective theory, the nature of the quantum phase transitions among various phases can be identified. Moreover, the general condition for the appearance of the recently proposed Pfaffian-like state can be realized from our effective action.

Figure 1

The schematic phase diagram at integer filling $\overline{n}=n_0$ in the weak-coupling regime. The phase boundaries of Kosterlitz-Thouless, Gaussian, and Ising types are denoted by the solid, dashed, and dotted lines, respectively.

Figure 2

The schematic phase diagram near integer filling $\overline{n}\simeq n_0$. The solid lines denote the commensurate-incommensurate transition with $z=2$.