Diagrammatics: lectures on selected problems in condensed by Michael V. Sadovskll

By Michael V. Sadovskll

The creation of quantum box idea equipment has ended in one of those “revolution” in condensed topic conception. This ended in the elevated value of Feynman diagrams or diagram strategy. It has now turn into valuable for execs in condensed subject thought to have a radical wisdom of this system. there are lots of solid books that disguise the final features of diagrammatic tools. even as, there was a emerging want for books that describe calculations and methodical “know how” of particular difficulties for newcomers in graduate and postgraduate classes. This exact number of lectures addresses this want. the purpose of those lectures is to illustrate the appliance of the diagram strategy to varied difficulties of condensed topic idea. a few of these difficulties aren't “finally” solved. however the improvement of effects from any element of this ebook could function a kick off point for a significant theoretical research.

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13 Spectral density in Fermi-gas (a) and in Fermi-liquid (b). (Lorentzian) peak at e = ep (quasiparticle energy), on the smooth background due to multi-particle excitations, as shown in Fig. 13 (b), while in an ideal gas of Fermions it reduces to J-function, shown in Fig. 13 (a). Note, that spectral densities of electrons in interacting systems can, in fact, be measured experimentally via photoemission with angular resolution (ARPES) 10 , which allows also to study the form of real Fermi surfaces, even for very complicated compounds 11 .

1989)]. 5 Electron self-energy, effective mass and damping of quasiparticles Our final aim is to calculate single-particle Green's function in a system with Coulomb (or also some other) interaction. g. via some partial summation of diagram series. What physical information can be obtained in this way? We know that the Green's function of free electrons Go(pe) has a pole at ep = ^ — fi. 46) Electron-Electron Interaction 29 where e p represents the spectrum of "renormalized" quasiparticles. ), we have neglected ImT,, which (as we shall see later) determines quasiparticle damping.

Shen. From Mott insulator to overdoped superconductor: Evolution of the electronic structure of cuprates studied by ARPES. Rev. Mod. Phys. 75, 473 (2003) Electron-Electron JC = Fig. 14 Interaction 51 + + Independent propagation of two particles in Fermi-liquid. -'s: + i i Fig. 15 Diagrammatic definition of the block V. can be cut by two particle lines. + Crossed out are diagrams, which two independent sum of diagrams, each reducing to the full single-particle Green's function G. 138) Minus sign before the second (exchange) term here is due to the antisymmetry of Fermions under permutations.

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