Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling

TL;DR

This paper develops a fermionic functional renormalization group formalism for one-dimensional lattice electron models, deriving flow equations and analyzing phase diagram evolution, especially under doping, with comparisons to existing theories and numerical data.

Contribution

It introduces a formalism for applying the functional renormalization group to lattice fermion models at arbitrary filling, including derivation of flow equations and analysis of phase transitions.

Findings

Lattice effects influence coupling constants through spectrum curvature.

The phase diagram evolution with doping is characterized.

Comparison with field theory and numerical results validates the approach.

Abstract

A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.