Lattice renormalization group approach to the quantum ordered states of the one-dimensional extended Hubbard model as a function of filling

One-dimensional interacting fermionic systems are usually studied in the continuum limit, with a spectrum linearized in the vicinity of the two Fermi points. In these approaches, lattice effects are mostly discarded, despite the fact that they may qualitatively affect the phase diagram of the models under study. We have developed a formalism based on the Fermionic Functional Renormalization Group for models defined on a lattice. One loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels have been derived. It is shown that lattice effects manifest themselves through the curvature of the spectrum, and through the dependence of the coupling constants on momenta. In this talk, we discuss the application of this method to the phase diagram of the one-dimensional extended Hubbard model as a function of filling. In particular, the fate of the Charge Bond Ordered Wave phase and the disappearance of Umklapp processes away from half-filling are investigated.