Quasi-particle linewidth close to a quantum critical point: Crossover from non-Fermi liquid to Fermi liquid behavior

Heavy fermion systems frequently display non-Fermi liquid behavior due to a nearby quantum critical point. A nested Fermi surface together with the remaining interaction between the carriers after the heavy particles are formed may give rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as $T_N \to 0$. The quasi-particle linewidth is calculated in the paramagnetic phase following an approach outlined by Virosztek and Ruvalds (Phys. Rev. B {\bf 42}, 4064 (1990)). The linewidth shows a crossover from non-Fermi liquid ($\sim T$) to Fermi liquid ($\sim T^2$) behavior with increasing nesting mismatch and decreasing temperature. The quasi-particle linewidth is a quantity relevant to the electrical resistivity and the width of the inelastic neutron scattering quasi-elastic peak.