diff --git a/content/presentations.md b/content/presentations.md index cd36144..d688fe3 100644 --- a/content/presentations.md +++ b/content/presentations.md @@ -64,7 +64,42 @@ in first quantization, we develop an effective QED Hamiltonian in a fermionic Fo ### Cyril Martins (LCPQ, Toulouse) -**TBA** +**An introduction to Dynamical Mean-Field Theory** + +The "famous" Hubbard model was conceived in the 1960s [1,2,3] to get +insight into how the Coulomb interactions between conduction electrons +(for instance, in 3d transition metals) may affect "their motion" on a +lattice, and thus induce insulating or magnetic properties in a solid. +In its simplest form, the one-orbital (or single-band) Hubbard model +contains only a hopping term t between neighboring sites and an on-site +repulsive interaction term U. And yet, key insights into the Mott +metal-insulator transition (MIT) -- when the Coulomb repulsion can turn +a system insulating [4] -- can already be obtained, especially since the +advent of Dynamical Mean-Field Theory (DMFT) around 1990 [5,6]. + +DMFT can be seen as a quantum many-body extension of classical +mean-field approaches. Its power is the non-perturbative description of +correlations, which allows treating arbitrary interaction strengths: +DMFT can then capture both the Fermi liquid and the Mott insulator, and +provides a spatial mean-field description of the transition between them +[7]. + +In this talk, we will provide an introduction to the DMFT formalism, +explain how the method can be implemented in practice and discuss the +MIT and the phase diagramm of the Hubbard model on an infinite Bethe +lattice (where DMFT equations are exact). + +[1] J. Hubbard, Proc. R. Soc. London, Ser. A 276, 238 (1963); J. +Hubbard, Proc. R. Soc. London, Ser. A 277, 237 (1964). +[2] M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963) +[3] J. Kanamori, Progress of Theoretical Physics 30, 275 (1963) +[4] N. F. Mott and R. Peierls, Proceedings of the Physical Society 49, +72 (1937); N. F. Mott, Proceedings of the Physical Society. Section A +62, 416 (1949). +[5] W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989). +[6] A. Georges and G. Kotliar, Phys. Rev. B 45, 6479 (1992) +[7] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. +Phys. 68, 13 (1996). ### Nicolas Laflorencie (LPT, Toulouse)