Singular Valence Fluctuations at a Kondo Destroyed Quantum Critical Point

Recent experiments on the heavy fermion superconductor $\backslash $beta-YbAlB4 have indicated that this compound satisfies quantum critical scaling [1]. Motivated by the observation of mixed valency in this material [2], we study the Kondo destruction physics in the mixed-valence regime [3] of a particle-hole asymmetric Anderson impurity model with a pseudogapped density of states. In the vicinity of the quantum critical point we determine the finite temperature spin and charge susceptibilities by utilizing a continuous time quantum Monte Carlo method [4] and the numerical renormalization group. We show that this mixed-valence quantum critical point displays a Kondo breakdown effect. Furthermore, we find that both dynamic spin and charge susceptibilities obey frequency over temperature scaling, and that the static charge susceptibility diverges with a universal exponent. Possible implications of our results for $\backslash $beta-YbAlB4 are discussed. [1] Matsumoto et al, Science \textbf{331}, 316 (2011). [2] Okawaet al, Physical Review Letters \textbf{104}, 247201 (2010). [3] J. H. Pixley, S. Kirchner, Kevin Ingersent and Q. Si, arXiv:1108.5227v1 (2011). [4] M. Glossop, S. Kirchner, J. H. Pixley and Q. Si, Phys. Rev. Lett. \textbf{107}, 076404 (2011).