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| Falicov–Kimball model | |
|---|---|
| Name | Falicov–Kimball model |
| Field | Condensed matter physics |
| Introduced | 1969 |
| Authors | Luis M. Falicov; John C. Kimball |
Falicov–Kimball model The Falicov–Kimball model was introduced in 1969 and is a paradigmatic lattice model in condensed matter physics that describes interacting itinerant and localized electrons, developed by Luis M. Falicov and John C. Kimball. It has played a central role in studies of metal–insulator transitions, charge order, and correlation effects and connects to research themes pursued at institutions such as Bell Labs, IBM, and universities like Harvard and Stanford. Influential researchers including Neville Mott, Philip W. Anderson, Sir Nevill F. Mott, and Walter Kohn have shaped the conceptual background that contextualizes the Falicov–Kimball model.
The Falicov–Kimball model occupies a position alongside models such as the Hubbard model, the Anderson impurity model, and the Kondo model in the study of correlated electrons, and it has been used in comparisons with works by John Hubbard, P. W. Anderson, and Jun Kondo. Its formulation was motivated by experimental observations in transition metal oxides, rare-earth compounds, and materials studied at laboratories like Argonne National Laboratory, Oak Ridge National Laboratory, and Lawrence Berkeley National Laboratory. The model has been cited in theoretical developments connected to the Dynamical Mean Field Theory program led by Gabriel Kotliar and Antoine Georges and in numerical studies associated with groups at Max Planck Institutes and École Normale Supérieure.
The Falicov–Kimball model is defined on a lattice such as the square lattice, cubic lattice, or Bethe lattice and comprises itinerant c-electrons and localized f-electrons with an on-site interaction; this Hamiltonian is often compared to the Hubbard Hamiltonian introduced by John Hubbard and the periodic Anderson Hamiltonian associated with P. W. Anderson. The standard Hamiltonian contains kinetic terms similar to tight-binding models used by Philip Anderson and Walter Kohn, a local on-site interaction term U reminiscent of Coulomb interactions discussed by Nevill Mott and Sir Nevill F. Mott, and a chemical potential term analogous to those in Bardeen–Cooper–Schrieffer theory studied by John Bardeen, Leon Cooper, and Robert Schrieffer. On lattices considered by Elliott H. Lieb and Barry Simon, the model can be written in second quantization language used by Julian Schwinger and Richard Feynman, facilitating connections to techniques developed by Lars Onsager and Lev Landau.
Exact solutions and rigorous results for the Falicov–Kimball model exist in special limits and low-dimensional cases and have been derived using methods related to those of Elliott H. Lieb, Barry Simon, and Michael Fisher. On the Bethe lattice in infinite dimensions, the model is soluble within Dynamical Mean Field Theory as developed by Georges and Kotliar, while one-dimensional chains relate to work by Hans Bethe and Nobel laureates such as Philip W. Anderson on integrable systems. At zero temperature and in classical limit regimes the model maps onto classical lattice gas problems studied by Lars Onsager and Rudolf Peierls and has rigorous phase results proved using techniques associated with Elliott Lieb and Barry Simon.
The model exhibits a variety of phases including charge-density-wave order, metal–insulator transitions, and phase separation phenomena that have been explored in the context of oxides investigated by John Goodenough and Clarence Zener and in rare-earth compounds studied by Kasuya and Yosida. Thermodynamic properties such as specific heat and compressibility are analyzed using approaches related to Landau theory as developed by Lev Landau and renormalization-group ideas introduced by Kenneth Wilson. Classical and quantum critical behavior in the model has been compared to universality classes classified by Leo Kadanoff and Michael Fisher, and its spectral functions and optical conductivities have been connected to experimental probes used in studies at synchrotrons like the Advanced Photon Source and facilities such as CERN.
Extensions include spinful versions, inclusion of phonons as in Holstein-type couplings studied by T. Holstein, hybridization terms akin to the periodic Anderson model by P. W. Anderson, and multi-band generalizations relevant to materials research by J. Zaanen and A. M. Oleś. Generalizations have been used in combination with methods developed by Antoine Georges, Gabriel Kotliar, and Dieter Vollhardt in Dynamical Mean Field Theory, and with cluster extensions pioneered by Thomas Maier and Mark Jarrell. Connections to disordered systems evoke studies by Phil Anderson on localization and to topological phases investigated by Charles Kane and Eugene Mele.
Numerical studies employ exact diagonalization techniques rooted in Lanczos algorithms developed by Cornelius Lanczos, Quantum Monte Carlo methods refined by Metropolis and Hubbard–Stratonovich transformations discussed by John Hubbard, and Dynamical Mean Field Theory impurity solvers such as numerical renormalization group by Kenneth Wilson and continuous-time Monte Carlo approaches advanced by Evert Gull. Cluster and density-matrix renormalization-group methods trace intellectual lineage to Steven White and Ulrich Schollwöck, while computational implementations leverage high-performance computing centers like Oak Ridge Leadership Computing Facility and NSF supercomputing resources.
The Falicov–Kimball model has been applied to interpret experiments on mixed-valence compounds, manganites studied by J. B. Goodenough, and charge-ordered materials probed in experiments at synchrotron facilities like the European Synchrotron Radiation Facility and Diamond Light Source. It informs analysis of transport and optical spectroscopy measurements carried out by research groups at MIT, Princeton University, and the University of Cambridge and has influenced theoretical modeling in collaborations involving institutions such as the Max Planck Society and CNRS. The model continues to inform studies bridging theoretical frameworks associated with Philip W. Anderson, Neville Mott, and Walter Kohn and experimental programs at major laboratories worldwide.
Category:Condensed matter physics models