We use a strong coupling expansion [1] to solve the one-dimensional extended t V model of fermions [2,3]. The model is solved for a range of densities, including both commensurate – where a charge density wave is present – and incommensurate densities. The first set consists not only of a trivial case of half filling. The method allows us to trace the transition from a Luttinger liquid phase to a Mott insulating phase. This simple yet powerful method is not based on Bethe ansatz and it works for both integrable and non-integrable systems.

References
[1] C.J. Hamer, Phys. Lett. B, 1979, 82, 75-78.
[2] G. Gómez-Santos, Phys. Rev. Lett., 1993, 70, 3780.
[3] R.G. Dias, Phys. Rev. B, 2000, 62, 7791.