Impurity quantum phase transitions

Abstract

Recent work is reviewed 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. Results are presented for a number of observables, obtained by both analytical and numerical renormalization group techniques, and connections made to experiments.

Acknowledgments

The author is grateful to Z. Gulacsi for the smooth organization the 3rd Summer School on Strongly Correlated Systems in Debrecen. Most of the work reviewed here is based on fruitful collaborations with R. Bulla, C. Buragohain, L. Fritz, M. Garst, W. Hofstetter, M. Kirćan, Th. Pruschke, A. Rosch, S. Sachdev, N. Tong and M. Troyer. The author also acknowledges illuminating discussions with L. Balents, S. Florens, A. C. Hewson. D. Logan, N. Read, Q. Si, D. Vollhardt, P. Wölfle, and W. Zwerger. Special thanks is to C. Lorenz for continued support during the writing of this article. This research was supported by the Deutsche Forschungsgemeinschaft through the Center for Functional Nanostructures Karlsruhe.