Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem

TL;DR

This paper develops a universal critical theory for the quantum phase transition in the asymmetric pseudogap Kondo model, identifying an upper-critical dimension and calculating critical properties using renormalization group methods.

Contribution

It introduces a new theoretical framework for the asymmetric pseudogap Kondo transition, highlighting the role of an upper-critical dimension and providing perturbative critical property calculations.

Findings

Identification of an upper-critical dimension in the impurity problem.

Derivation of critical properties using perturbative renormalization group.

Agreement of theoretical results with numerical simulations.

Abstract

Impurity moments coupled to fermions with a pseudogap density of states display a quantum phase transition between a screened and a free moment phase upon variation of the Kondo coupling. We describe the universal theory of this transition for the experimentally relevant case of particle-hole asymmetry. The theory takes the form of a crossing between effective singlet and doublet levels, interacting with low-energy fermions. Depending on the pseudogap exponent, this interaction is either relevant or irrelevant under renormalization group transformations, establishing the existence of an upper-critical "dimension" in this impurity problem. Using perturbative renormalization group techniques we compute various critical properties and compare with numerical results.