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| Kondo model | |
|---|---|
| Name | Kondo model |
| Field | Condensed matter physics |
| Introduced | 1964 |
| Contributors | Jun Kondo |
| Keywords | magnetic impurity, resistivity minimum, renormalization group, Kondo effect |
Kondo model The Kondo model is a theoretical model in Condensed matter physics describing a localized magnetic impurity coupled to a sea of conduction electrons, introduced to explain anomalies in low-temperature resistivity; it links phenomena studied in Jun Kondo's work to techniques developed for the Renormalization Group, Andrei Tsvelik's integrability approaches, and the experimental puzzles seen in Neutron scattering and Scanning tunneling microscopy. The model shaped research directions involving Ken Wilson's numerical renormalization group, influenced studies related to the Anderson impurity model, and connected to developments in Quantum dot experiments, Heavy fermion compounds, and the physics of High-temperature superconductivity.
The Kondo model considers a localized spin-1/2 impurity interacting via exchange coupling with conduction electrons in a metal, addressing the resistivity minimum observed in metals with dilute magnetic impurities and laying groundwork that interfaces with the Anderson impurity model, Ruderman–Kittel–Kasuya–Yosida interactions, and concepts used in Quantum impurity problems. From its inception the model influenced theoretical work by Philip W. Anderson, Nikolay Bogoliubov, and Alexander Zamolodchikov in integrable systems, as well as experimental programs at institutions like Bell Labs, CERN, IBM Research, and Los Alamos National Laboratory.
The anomaly of a low-temperature upturn in resistivity for metals containing magnetic atoms was reported in experiments at Bell Labs and other laboratories and motivated Jun Kondo's 1964 calculation that showed logarithmic temperature dependence via third-order scattering diagrams; contemporaneous conceptual advances came from studies by Lev Landau's Fermi liquid theory, early many-body work by Gunnar K. O. Lundquist, and scattering formalism developed in John Bardeen-influenced research. The resolution of the resulting divergence spurred the development of the Renormalization Group by Ken Wilson and integrable approaches by Nicolai Andrei and Paul Wiegmann, while experimental confirmation emerged through techniques at Rutherford Appleton Laboratory, Stanford University, and Brookhaven National Laboratory.
The Hamiltonian of the Kondo model comprises a conduction electron term and a local exchange term J S·s(0), where S is the impurity spin and s(0) is the conduction electron spin density at the impurity site; this formulation sits in relation to the s-d model and the Anderson model via Schrieffer–Wolff transformation pioneered by Roger Schrieffer and Philip W. Anderson. The model admits variants involving anisotropic exchange studied in the context of the XXZ spin chain and ties to exact solutions obtained through the Bethe ansatz by Nikolai Andrei and Paul Wiegmann, merging insights from Integrable systems and techniques developed by Hans Bethe and Ludwig Faddeev.
Perturbative approaches beginning with Kondo's calculation employed diagrammatic techniques refined by practitioners like G. D. Mahan and Piers Coleman, while nonperturbative resolution required the Numerical renormalization group developed by Ken Wilson, the analytical Bethe ansatz solved by Nicolai Andrei and Paul Wiegmann, and the Conformal field theory machinery applied by Ian Affleck and Alexander Ludwig. Additional solution frameworks include the Poor man's scaling method of Philip W. Anderson, variational wavefunctions inspired by John Hubbard and Walter Kohn, and quantum Monte Carlo simulations advanced at Argonne National Laboratory and University of Illinois.
The hallmark prediction is the logarithmic increase of resistivity at low temperatures followed by the formation of a many-body singlet below the Kondo temperature TK, affecting measurable quantities in Transport measurements, Magnetic susceptibility experiments, and Specific heat probes; signatures were identified using Scanning tunneling microscopy on single adatoms manipulated in IBM Research experiments and in Quantum dot conductance studies at Yale University and Harvard University. The model underpins understanding of Fano resonance lineshapes in tunneling spectra seen in Angle-resolved photoemission spectroscopy setups and influences thermoelectric responses measured at facilities like Max Planck Institute for Solid State Research.
Extensions include the multichannel Kondo model related to non-Fermi-liquid physics studied by Ian Affleck and Andrey Tsvelik, the two-impurity Kondo model addressing inter-impurity correlations explored by David Jones and Andrei M. Tsvelik, and lattice generalizations such as the Kondo lattice central to theories of Heavy fermion materials investigated by groups at Bell Labs and Los Alamos National Laboratory. Related models include the Anderson impurity model connected via Schrieffer–Wolff transformation, the Coqblin–Schrieffer model for orbital degeneracy, and connections to Luttinger liquid physics in one-dimensional conductors studied at University of Cambridge and Ecole Normale Supérieure.
Realizations range from dilute magnetic alloys studied historically in metallurgy labs and at Bell Labs to engineered single-impurity systems created with Scanning tunneling microscopy at IBM Research and semiconductor Quantum dot devices probed at Stanford University and MIT. Applications influence design principles in Spintronics research at Hitachi and NEC Corporation, inform interpretations of spectroscopic data from Brookhaven National Laboratory and Synchrotron Radiation Source facilities, and guide exploration of correlated phases in Ce-based compounds and Yb-based compounds synthesized at institutions like Max Planck Society and Tohoku University.