Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes

We develop two theoretical approaches for dealing with the low-energy effects of the repulsive interaction in one-dimensional electron systems. Renormalization Group methods allow us to study the low-energy behavior of the unscreened interaction between currents of well-defined chirality in a strictly one-dimensional electron system. A dimensional regularization approach is useful, when dealing with the low-energy effects of the long-range Coulomb interaction. This method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1. We can also compare these approaches with the Luttinger model, to analyze the effects of the short-range term in the interaction. Thanks to these methods, we are able to discuss the effects of a strong magnetic field B in quasi one-dimensional electron systems, by focusing our attention on Carbon Nanotubes. Our results imply a variation with B in the value of the critical exponent α for the tunneling density of states, which is in fair agreement with that observed in a recent transport experiment involving carbon nanotubes. The dimensional regularization allows us to predict the disappearance of the Luttinger liquid, when the magnetic field increases, with the formation of a chiral liquid with α = 0.