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| Kondo lattice model | |
|---|---|
| Name | Kondo lattice model |
| Field | Condensed matter physics |
| Introduced | 1960s |
| Key people | Jun Kondo, Kenneth G. Wilson, Philip W. Anderson, John Hubbard, Yoichi Nagaoka |
| Related models | Kondo model; Anderson lattice; Hubbard model; Heisenberg model; Falicov–Kimball model |
Kondo lattice model The Kondo lattice model describes arrays of localized magnetic moments interacting with itinerant conduction electrons and underpins understanding of heavy fermion compounds, magnetic order, and unconventional superconductivity. It connects insights from the work of Jun Kondo, Philip W. Anderson, John Hubbard, Kenneth G. Wilson, and others, and plays a central role in theoretical treatments that also involve the Heisenberg model, Anderson impurity model, and the Hubbard model.
The Kondo lattice model emerged to generalize the single-impurity Kondo effect to periodic arrays of magnetic moments present in materials such as CeCu6, CeAl3, UPt3, URu2Si2, and YbRh2Si2. Early theoretical developments drew on techniques from studies of the Anderson model, renormalization group methods by Kenneth G. Wilson, and perturbative analysis by Jun Kondo. The model is central to explaining competing tendencies toward Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions and Kondo screening, and informs interpretations of experiments by groups at institutions like Los Alamos National Laboratory, Max Planck Institute for Chemical Physics of Solids, and CNRS laboratories.
The canonical Hamiltonian couples localized spin operators on a lattice (frequently modeled after rare-earth ions in compounds such as CeCoIn5 and CeRhIn5) to conduction electron operators as in formulations inspired by the s-d model and the Anderson lattice model. Typical terms reference tight-binding conduction bands as in work on graphene and cuprates and local exchange coupling reminiscent of the Kondo model; additional terms often include kinetic energy from the tight-binding model, local Coulomb repulsion akin to the Hubbard U in the Hubbard model, and direct Heisenberg exchange as in the Heisenberg model. Variants introduce orbital degeneracy found in actinides and lanthanides, crystal-field splitting described in studies of crystal field theory, and spin–orbit coupling prominent in topological insulators and iridates.
The model exhibits competition between Kondo singlet formation and magnetic order mediated by RKKY interactions, leading to phases including heavy Fermi liquids observed in CeCu2Si2, antiferromagnetism seen in CeRhIn5, and exotic superconductivity as in UPt3 and CeCoIn5. Quantum critical points connecting these phases relate to concepts from the theory of quantum phase transitions and have been explored in relation to the Hertz–Millis theory and local quantum criticality proposals associated with Qimiao Si. Non-Fermi liquid behavior is connected to ideas from Sachdev–Ye–Kitaev model analogies, while Kondo insulators such as SmB6 tie into discussions of topological phases and topological Kondo insulator proposals.
Analytical and numerical tools applied include perturbative renormalization group approaches pioneered by Kenneth G. Wilson and Philip W. Anderson, large-N techniques developed following Nobel Prize in Physics–level methods, slave-boson mean-field theory related to work by N. Read and D. M. Newns, dynamical mean-field theory (DMFT) connected to efforts at Georges Kotliar’s group, and quantum Monte Carlo studies with algorithmic advances by teams including Scalapino and Assaad. Exact diagonalization, density matrix renormalization group (DMRG) inspired by Steven R. White, and matrix product state methods draw on computational innovations from institutions such as Oak Ridge National Laboratory and Lawrence Berkeley National Laboratory. Field-theoretical descriptions leverage techniques from conformal field theory and the renormalization group.
Real materials exhibiting Kondo lattice physics include heavy fermion families like Ce-based compounds (e.g., CeCu6, CeAl3, CeCoIn5), YbRh2Si2, URu2Si2, and Kondo insulators such as SmB6. Experimental probes include angle-resolved photoemission spectroscopy (ARPES) groups at ALS and ESRF, scanning tunneling microscopy (STM) studies from labs like IBM Research, neutron scattering experiments at facilities such as Institut Laue–Langevin and Oak Ridge National Laboratory's HFIR, and transport and thermodynamic measurements performed at Los Alamos National Laboratory and MPI. Signatures include enhanced electronic specific heat (γ) reminiscent of heavy quasiparticles, Fermi surface reconstruction detected via de Haas–van Alphen experiments often conducted at National High Magnetic Field Laboratory, and Kondo coherence peaks seen in STM and ARPES.
Extensions include the periodic Anderson lattice model, multi-orbital generalizations relevant to actinide chemistry, the Falicov–Kimball model for mixed valence, and coupling to phonons as explored in Holstein model contexts. The interplay with spin–orbit coupling yields connections to topological insulators and proposals for topological Kondo insulators in materials like SmB6. Low-dimensional variants intersect with research on quantum wires, quantum dots and cold-atom emulations pursued at institutions such as MIT and Harvard University. Kondo physics also appears in nanostructures studied by groups at CERN collaborations on correlated electron systems and in molecular magnets explored at Max Planck Institute for Chemical Physics of Solids.
Active challenges include microscopic understanding of quantum criticality as debated in the literature by researchers like Qimiao Si and Piers Coleman, the mechanisms of unconventional superconductivity in heavy fermions investigated by teams at University of Cambridge and Rutgers University, the nature of topological states in Kondo insulators examined by groups at University of British Columbia and Princeton University, and real-time dynamics in nonequilibrium Kondo lattices studied with ultrafast spectroscopy at facilities such as SLAC National Accelerator Laboratory. Progress leverages cross-disciplinary methods from quantum information theory, advanced numerical platforms at Argonne National Laboratory, and collaborative experimental campaigns at synchrotrons like Diamond Light Source.