Critical charge fluctuations in a pseudogap Anderson model

Abstract

The Anderson impurity model with a density of states $\rho (\epsilon )\propto |\epsilon {|}^r$ containing a power-law pseudogap centered on the Fermi energy ($\epsilon =0$) features for $0<r<1$ a Kondo-destruction quantum critical point (QCP) separating Kondo-screened and local-moment phases. The observation of mixed valency in quantum critical $\beta$-YbAlB${}_4$ has prompted study of this model away from particle-hole symmetry. The critical spin response associated with all Kondo destruction QCPs has been shown to be accompanied, for $r=0.6$ and noninteger occupation of the impurity site, by a divergence of the local charge susceptibility on both sides of the QCP. In this work, we use the numerical renormalization-group method to characterize the Kondo-destruction charge response using five critical exponents, which are found to assume nontrivial values only for $0.55\lesssim r<1$. For $0<r\lesssim 0.55$, by contrast, the local charge susceptibility shows no divergence at the QCP, but rather exhibits nonanalytic corrections to a regular leading behavior. Both the charge critical exponents and the previously obtained spin critical exponents satisfy a set of scaling relations derived from an ansatz for the free energy near the QCP. These critical exponents can all be expressed in terms of just two underlying exponents: the correlation-length exponent $\nu (r)$ and the gap exponent $\Delta (r)$. The ansatz predicts a divergent local charge susceptibility for $\nu <2$, which coincides closely with the observed range $0.55\lesssim r<1$. Many of these results are argued to generalize to interacting QCPs that have been found in other quantum impurity models.

8 pages, 4 figures

References in corpus (8)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Heavy Fermions and Quantum Phase Transitions
• Fermi-surface collapse and dynamical scaling near a quantum critical point
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• Kondo physics and dissipation: A numerical renormalization-group approach to Bose-Fermi Kondo models
• Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory
• Quantum phase transitions in a pseudogap Anderson-Holstein model
• Quantum phase transitions in a resonant-level model with dissipation: Renormalization-group studies