Interacting Electrons: Theory and Computational Approaches

Description

Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments. Review: The major book for practical many body theory and computation for condensed matter physics - This is the clearest, most complete presentation available for practical many body methods in condensed matter physics. It's main strength is to have all the main methods together in a unified way Review: Compute Accurate Spectra for even Actinides - - 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.