Interacting Electrons: Theory and Computational Approaches

- Introduces the spectral representation of one particle Green’s and uses it as a benchmark to introduce a two particle correlation function.- Derives the Dyson equation and reformulates it using a geometric series technique to emphasize the impurity scattering.- Defines grand canonical potential as a functional of a Green’s function to more formally establish conservation laws and identities that subsequently derived equations need to obey.- Closely examines full self energy to write the exchange and correlation energy in terms of familiar functions to make physics relevant approximations more identifiable.- The exchange and correlation energy is approximated as the product of the screening potential and Green’s function (GW approximation), which motivates the creation of the irreducible Heidin equations used in a practical calculation:From a preliminary Kohn and Sham Density Functional theory, determine the eigenfunctions for each band and construct the Lehman representation of the non interacting Green’s function. Use subsequent polarizability and dielectric function to create the Screening Coulomb interaction. And through the GW approximation, we output the Green's function and are able to calculate a host of properties about our system.- A similar algorithm allows a calculation of the correlation function, which is needed to calculate spectroscopic properties. The text later introduces dynamical mean field theory to calculate Lanthanides and Actinides since strongly correlated systems such as d and f electron elements show the pitfalls of the GW approximation.

good

The contents of the book are good. However it arrived physically damaged, the envelope was torn and the edges of the cover of the book are bent.