Multiscale fluctuations near a Kondo breakdown quantum critical point

We study the Kondo-Heisenberg model using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero-temperature quantum critical point separating a spin liquid phase where the f-conduction hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase, namely, a uniform hybridization when the band masses of the conduction electrons and the f spinons have the same sign and a modulated one when they have opposite sign. For the uniform case, we show that above a very small Fermi-liquid temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent $z=3$, giving rise to a specific-heat coefficient that diverges logarithmically in temperature, as well as a conduction-electron inverse lifetime that has a T log T behavior. Because the f spinons do not carry current, but act as an effective bath for the relaxation of the current carried by the conduction electrons, the latter result also gives rise to a T log T behavior in the resistivity. This behavior is consistent with observations in a number of heavy fermion metals.