  One-dimensional strongly correlated electron systems coupled via transverse
hopping and presence of interband interactions can converge to a Luttinger
liquid state or diverge to an even more intricate behavior, as a Mott state.
Explicit consideration of the renormalization group (RG) flow of the Fermi
points in the Fermi surface, turns the classification of phase transitions more
challenging. We reconsider the recent paper for the spinless case [E. Correa
and A. Ferraz, Eur. Phys. J. B 87 (2014) 51], where RG flow equations are
derived in a cutoff-dependent form up to two-loops order. We demonstrate that
the cutoff-dependence can be removed by rewriting the RG flow equations in
terms of the energy scale variable. In our paper, the RG flow equations assume
a cutoff-independent form and leads to fixed points independent of cutoff
choice. The consequence is the invariance under cutoff transformations, more
suitable for classifying universality classes and phase transitions.
