Quantum scaling in many-body systems

A book is presented on quantum phase transition (QFT), concentrated on the transition occurring in strongly correlated electronic systems. The first chapter presents the scaling theory of quantum critical phenomena. In the initial chapters, general ideas and basic models of statistical mechanics are introduced. The renormalization group is carefully presented in this momentum version and real space formulation, by applying these methods to specific and basic problems. For the momentum space formulation the original Wilson-Landau functional and the ε-expansion in the one-loop approximation is considered.The real space renormalization group is presented in the block version through a study of the Ising model in a transverse field. The concept of coherence temperature, related to a quantum critical point, is introduced and it importance emphasized as it represents the characteristic temperature of a Kondo lattice, in distinction to the Kondo temperature of the one-impurity problem. The metal-insulator transition which occur at zero temperature is studied. The non-linear sigma model is discussed. The book ends with a discussion on first order zero temperature transitions