Critical charge fluctuations in a pseudogap Anderson model

TL;DR

This paper investigates the critical charge fluctuations in a pseudogap Anderson model near a quantum critical point, revealing how charge and spin responses behave differently depending on the pseudogap exponent r, with implications for understanding quantum criticality.

Contribution

The study characterizes charge critical exponents in the pseudogap Anderson model using numerical renormalization-group methods, revealing nontrivial behavior for 0.55 ≤ r < 1 and scaling relations linking charge and spin responses.

Findings

Charge susceptibility diverges for 0.55 ≤ r < 1.

No divergence in charge susceptibility for 0 < r < 0.55.

Scaling relations connect charge and spin critical exponents.

Abstract

The Anderson impurity model with a density of states $\rho(\varepsilon) \propto |\varepsilon|^r$ containing a power-law pseudogap centered on the Fermi energy ($\varepsilon = 0$) 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.