Impurity Quantum Phase Transitions

TL;DR

This review discusses recent advances in understanding quantum phase transitions in impurity models with fermionic and bosonic baths, highlighting boundary critical phenomena and the role of competing interactions.

Contribution

It synthesizes recent analytical and numerical renormalization group results on impurity quantum phase transitions, emphasizing new insights into critical fixed points and experimental relevance.

Findings

Identification of unstable fixed points at quantum phase transitions

Impurity models exhibit both lower-critical and upper-critical dimensions

Epsilon-expansion techniques are applicable to certain impurity transitions

Abstract

We review recent work on continuous quantum phase transitions in impurity models, both with fermionic and bosonic baths - these transitions are interesting realizations of boundary critical phenomena at zero temperature. The models with fermion bath are generalizations of the standard Kondo model, with the common feature that Kondo screening of the localized spin can be suppressed due to competing processes. The models with boson bath are related to the spin-boson model of dissipative two-level systems, where the interplay between tunneling and friction results in multiple phases. The competition inherent to all models can generate unstable fixed points associated with quantum phase transitions, where the impurity properties undergo qualitative changes. Interestingly, certain impurity transitions feature both lower-critical and upper-critical "dimensions" and allow for epsilon-type expansions. We present results for a number of observables, obtained by both analytical and numerical renormalization group techniques, and make connections to experiments.