Quantum criticality in the two-channel pseudogap Anderson model: A test of the non-crossing approximation

TL;DR

This paper studies the quantum phase transitions in the pseudogap two-channel Anderson model using the noncrossing approximation and numerical renormalization group, confirming the NCA's reliability and revealing critical behavior.

Contribution

It extends the noncrossing approximation analysis to the pseudogap two-channel Anderson model, demonstrating its effectiveness in capturing phase diagrams and critical exponents.

Findings

NCA reproduces phase diagram and critical exponents accurately.

Dynamical susceptibility and Green's function show frequency-over-temperature scaling.

NCA results agree well with NRG and exact solutions.

Abstract

We investigate the dynamical properties of the two-channel Anderson model using the noncrossing approximation (NCA) supplemented by numerical renormalization-group calculations. We provide evidence supporting the conventional wisdom that the NCA gives reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. We extend the analysis to the pseudogap two-channel model describing a semi-metallic host with a density of states that vanishes in power-law fashion at the Fermi energy. This model exhibits continuous quantum phase transitions between weak- and strong-coupling phases. The NCA is shown to reproduce the correct qualitative features of the pseudogap model, including the phase diagram, and to yield critical exponents in excellent agreement with the NRG and exact results. The forms of the dynamical magnetic susceptibility and impurity Green's function at the fixed points are suggestive of frequency-over-temperature scaling.