Cellular Dynamical Mean Field Theory Of The Holstein Polaron Problem

We show how to set up a Cellular Dynamical Mean Field Theory for the Holstein's polaron problem using the exact solution of a cluster of n sites embedded in a Weiss's field. We show that a restricted basis, that allows excitations of phonons only for n sites at a time, reproduces exactly the equations of the n-site Dynamical Mean Field Theory, and enables to check the proposed decoupling scheme of the Green's functions via Exact Numerical Diagonalizations. We introduce a real space formulation of the Cellular Dynamical Mean Field Theory that applies to any lattice with or without periodic boundary conditions and that allows to partition the lattice into different kinds of clusters.

This book is a short introduction to the Dynamical Mean-Field Theory for strongly correlated electrons. Its purpose is to focus on various local decoupling schemes in order to derive a self-consistent approximation and to map the lattice problem onto an impurity problem. Hubbard, Holstein, and Falicov-Kimball models are mainly used to provide examples of calculation. Numerous basic c/c++ programs are given along the book to develop confidence in computing actual numerical results.

This book reviews recent developments in the field of polarons, starting with the basics and covering a number of active directions of research. It integrates theory and experimental results.

An enormous theoretical effort has been made to treat electron-phonon coupled systems, with particular emphasis on Many Body aspects for dense electron systems, taking into account continuum as well as lattice polaron effects. Treating such aspects of polaron theory has been made possible because of powerful Many Body techniques which include: Exact Diagonalization techniques, Quantum Monte Carlo approaches, Density Matrix renormalization group and Dynamical Mean Field Theory. All these advances in polaron theory needed to be accompanied by: (i) an equally important advance in material research which produced many new materials such as the high Tc cuprates, the manganites and nickelates and the fullerines; (ii) as well as significant advances in the refinement of experimental analysis and, in particular, the spectroscopic means such as Angel Resolved Photoemission Spectroscopy, X Ray Absorption Spectroscopy (EXAFS, XANES), Pulsed Neutron Diffraction measurements allowing to study the local dynamical lattice de-formations and optical spectroscopy including time resolved measurements. The scope and purpose of this publication is to review both these theoretical and experimental advances which occurred over the last few decades and to introduce the study of such systems, where both strong electron-electron correlations and large electron-phonon coupling strengths play important roles.

The features and mechanism of Colossal Magnetoresistance, or CMR, in manganese oxides as well as device physics are highlighted in this book, with a focus on tunneling MR for some artificial structures. Underlying new science, such as tunable electron-lattice interaction in a metal and roles of orbital degrees of freedom in producing an unconventional metallic feature, is also discussed. The book provides a systematic exploration of the CMR materials and an extensive investigation of the electronic phenomena of those compounds by various experimental means.

A distinctive introduction to the principles governing polaron science for experimental and theoretical graduate students and researchers.

Theory of Superconductivity: From Weak to Strong Coupling leads the reader from basic principles through detailed derivations and a description of the many interesting phenomena in conventional and high-temperature superconductors. The book describes physical properties of novel superconductors, in particular, the normal state, superconducting crit

This book first introduces a single polaron and describes recent achievements in analytical and numerical studies of polaron properties in different e-ph models. It then describes multi-polaron physics as well as many key physical properties of high-temperature superconductors, colossal magnetoresistance oxides, conducting polymers and molecular nanowires, which were understood with polarons and bipolarons.