The volume contains the lectures delivered at the “XV Training Course in the Physics of Strongly Correlated Systems”, held in Vietri sul Mare (Salerno) Italy, in October 2010. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date
monographies of relevant subjects in the field of Condensed Matter Physics. Contributions include: The Density Matrix Renormalization Group and its Time-Dependent Variants (Model
Hamiltonians, Exact Diagonalization, Truncated Diagonalization: the Numerical, Renormalization Group idea, The Density Matrix Truncation: the kernel of the DMRG, The DMRG algorithm, When and why does the DMRG work?, The time-dependent DMRG, Alps DMRG). Strong Correlations in Solids: A Survey of Experimental Facts (Electrons in metals, Superconductivity, Low-dimensional physical systems). Static and Dynamic Variational Principles for Strongly Correlated Electron Systems (Models and variational methods, Static variational principle, Using the Ritz principle to construct approximations; Dynamical quantities; Self-energy-functional theory; Consistency, symmetry and systematics; Bath sites and dynamical mean-field theory).