Universal crossovers and critical dynamics of quantum phase transitions: A renormalization group study of the pseudogap Kondo problem

TL;DR

This paper uses renormalization group methods to analytically study universal crossover functions and critical dynamics in the pseudogap Kondo problem, achieving agreement with numerical simulations and extending understanding of quantum phase transitions.

Contribution

It introduces a renormalization group approach to calculate universal crossover functions for the pseudogap Kondo problem, including finite-temperature dynamics, with results matching numerical simulations.

Findings

Analytical crossover functions agree with NRG results

Progress made in finite-temperature low-frequency dynamics analysis

Method applicable to other quantum phase transitions

Abstract

The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment with a power-law density of states, displays continuous quantum phase transitions between free and screened moment phases. In this paper we employ renormalization group techniques to analytically calculate universal crossover functions, associated to these transitions, for various observables. Quantitative agreement with the results of Numerical Renormalization Group (NRG) simulations is obtained for temperature-dependent static and zero-temperature dynamic quantities, at and away from criticality. In the notoriously difficult realm of finite-temperature low-frequency dynamics, usually inaccessible to both NRG and perturbative methods, we show that progress can be made by a suitable renormalization procedure in the framework of the Callan-Symanzik equations. Our general strategy can be extended to other zero-temperature phase transitions, both in quantum impurity models and bulk systems.