Quantum Boltzmann equation study for the Kondo breakdown quantum critical point

We develop the quantum Boltzmann equation approach for the Kondo breakdown quantum critical point, involved with two bands for conduction electrons and localized fermions. Particularly, the role of vertex corrections in transport is addressed, crucial for non-Fermi liquid transport with temperature linear dependence. Only one band of spinons may be considered for scattering with gauge fluctuations, and their associated vertex corrections are introduced in the usual way, where the divergence of self-energy corrections is cancelled by that of vertex corrections, giving rise to a physically meaningful result in the gauge invariant expression for conductivity. On the other hand, two bands should be taken into account for scattering with hybridization excitations, giving rise to coupled quantum Boltzmann equations. We find that vertex corrections associated with hybridization fluctuations turn out to be irrelevant due to the heavy mass of spinons in the so called decoupling limit, consistent with the diagrammatic approach showing non-Fermi liquid transport.