This book offers a compact tutorial on basic concepts and tools in quantum many-body physics, and focuses on the correlation effects produced by mutual interactions. The content is divided into three parts, the first of which introduces readers to perturbation theory. It begins with the simplest examples-hydrogen and oxygen molecules-based on their effective Hamiltonians, and looks into basic properties of electrons in solids from the perspective of localized and itinerant limits. Readers will also learn about basic theoretical methods such as the linear response theory and Green functions. The second part focuses on mean-field theory for itinerant electrons, e.g. the Fermi liquid theory and superconductivity. Coulomb repulsion among electrons is addressed in the context of high-Tc superconductivity in cuprates and iron pnictides. A recent discovery concerning hydride superconductors is also briefly reviewed. In turn, the third part highlights quantum fluctuation effects beyond the mean-field picture. Discussing the dramatic renormalization effect in the Kondo physics, it provides a clear understanding of nonperturbative interaction effects. Further it introduces readers to fractionally charged quasi-particles in one and two dimensions. The last chapter addresses the dynamical mean field theory (DMFT). The book is based on the author's long years of experience as a lecturer and researcher. It also includes reviews of recent focus topics in condensed matter physics, enabling readers to not only grasp conventional condensed matter theories but also to catch up on the latest developments in the field.

One-dimensional quantum systems show fascinating properties beyond the scope of the mean-field approximation. However, the complicated mathematics involved is a high barrier to non-specialists. Written for graduate students and researchers new to the field, this book is a self-contained account of how to derive the exotic quasi-particle picture from the exact solution of models with inverse-square interparticle interactions. The book provides readers with an intuitive understanding of exact dynamical properties in terms of exotic quasi-particles which are neither bosons nor fermions. Powerful concepts, such as the Yangian symmetry in the Sutherland model and its lattice versions, are explained. A self-contained account of non-symmetric and symmetric Jack polynomials is also given. Derivations of dynamics are made easier, and are more concise than in the original papers, so readers can learn the physics of one-dimensional quantum systems through the simplest model.

Heavy electrons are found among a number of lanthanide and actinide compounds, and are characterized by a large effective mass which becomes comparable to the mass of a muon. Heavy electrons exhibit rich phenomena such as unconventional superconductivity, weak anti- ferromagnetism, or pseudo meta-magnetism. This book is intended not only as a monograph, but can readily serve as an advanced textbook on theoretical and experimental physics of strongly correlated electrons. Over the last two decades, heavy electrons have been the focus of very active experimental and theoretical studies. Many established ideas and techniques have been insufficient to describe and understand heavy electrons and their impact properly. On the theoretical side, quantum fluctuations make mean-field theories difficult to handle, while on the experimental side, extreme conditions such as strong magnetic fields and pressure at ultra-low temperatures may be required. Heavy electron systems as described in this book offer a case study for applying and testing most of the major tools in theoretical and experimental condensed matter physics. Graduate students and researchers working on strongly correlated condensed matter systems will find in this book a comprehensive introduction and many examples how conventional concepts of solids may work or not work, and how they can be refined and sharpened in the context of heavy electron systems.