Local density of states of the interacting resonant level model at zero temperature

The Anderson single impurity model, including its Kondo limit, can be seen as the hydrogen atom for correlated systems. Its most striking feature is the universal scaling of its low-energy properties governed by the appearance of a single emergent scale, the Kondo temperature T_K . In this work, we demonstrate the emergence of a second independent energy scale in a quantum impurity model, the interacting resonant level model, which is equivalent to the anisotropic Kondo model. We study the local density of states at the impurity site in the ground state (zero temperature limit) of the model. We see collapse of data onto universal curves at low energies, however this is only achieved by defining a second low-energy scale with a different power law dependence on model parameters than the Kondo temperature. We provide an exact expression for this second critical exponent. We also report on a splitting of the central resonance as the interaction strength is increased in the absence of any external magnetic field in the model.