Strongly Correlated Systems [electronic resource] : Theoretical Methods /
Avella, Adolfo.editor.
Mancini, Ferdinando.editor.
The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.
Strongly Correlated Systems; Preface; Contents; Foreword; Chapter 1 Density Functional Theory: A Personal View; 1.1 Introduction; 1.2 The Early Years: The Density as a Basic Variable; 1.3 Towards an ``Approximate Practical Method''; 1.4 Density Functional Formalism; 1.4.1 Single-Particle Description ofa Many-Particle System; 1.4.2 Approximations to Exc; 1.4.3 Exchange-Correlation Energy, Exc; 1.4.4 DF Theory in Retrospect; 1.5 The Beryllium Dimer; 1.5.1 The Story to Late 1979; 1.5.2 1980-1984; 1.5.3 After 1984; 1.6 Concluding Remarks; References
Chapter 2 Projected Wavefunctions and High Tc Superconductivity in Doped Mott Insulators2.1 Introduction; 2.2 Hubbard Model and Projected Wavefunctions; 2.3 Particle-hole Asymmetry in Doped Mott Insulators; 2.4 Gutzwiller Approximation; 2.5 Superconducting Ground State; 2.5.1 Energy Gap; 2.5.2 Order Parameter; 2.6 Momentum Distribution; 2.7 Electronic Excitations and Spectral Properties; 2.7.1 Nodal Fermi Velocity; 2.7.2 Spectral Function; 2.7.3 Sum Rules; 2.7.4 Fermi Surface; 2.8 Superfluid Density; 2.8.1 Doping Dependence of Ds; 2.8.2 Temperature Dependence of Ds
2.9 Disorder and Strong Correlations2.10 Competing Orders: Antiferromagnetism; 2.11 Conclusion; References; Chapter 3 The Pseudoparticle Approach to Strongly Correlated Electron Systems; 3.1 Introduction; 3.2 Pseudoparticle Representations of Quantum Operators; 3.2.1 Spin Operators; 3.2.1.1 Fermionic Representations of S=1/2 Spins; 3.2.2 Electron Operators; 3.2.2.1 Barnes's Representation; 3.2.2.2 Kotliar and Ruckenstein Representation; 3.2.2.3 Spin-Rotation Invariant Representation; 3.2.2.4 Spin- and Charge-Rotation-Invariant Formulation; 3.2.2.5 Gauge Symmetry and Radial Slave Boson Fields
3.3 Mean-Field Approximations3.3.1 Saddle-Point Approximation to the Barnes Representation; 3.3.1.1 Kondo Effect in the Anderson Impurity Model; 3.3.1.2 Heavy Fermions in the Anderson Lattice Model; 3.3.2 Saddle-Point Approximation to the KRRepresentation; 3.3.2.1 Mott-Hubbard Metal-Insulator Transition; 3.3.2.2 Magnetic Order in the Anderson Lattice Model; 3.4 Fluctuation Corrections to the Saddle-Point Approximation: SRI Representationof the Hubbard Model; 3.4.1 Magnetic and Stripe Phases; 3.5 Conserving Self-Consistent Approximations; 3.5.1 General Properties
3.5.2 Exact Infrared Properties of PseudoparticlePropagators3.5.3 Fock Space Projection in Saddle-PointApproximation; 3.5.4 Noncrossing Approximation (NCA); 3.5.4.1 Anderson Impurity Model for U: NCA; 3.5.4.2 Anderson Impurity Model with Finite U: SUNCA; 3.5.5 Conserving T-Matrix Approximation (CTMA); 3.5.5.1 Construction of the CTMA; 3.5.5.2 Principal Results; 3.6 Renormalization Group Approaches; 3.6.1 ``Poor Man's Scaling"" in the Equilibrium Kondo Model; 3.6.2 Functional RG for the Kondo Model Outof Equilibrium; 3.6.3 RG Approach to the Kondo Modelat Strong Coupling
3.6.4 Functional RG Approach to Frustrated Heisenberg Models
"With 147 figures."
Includes bibliographical references and index.
The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.
Solid state physics.
Spectroscopy.
Microscopy.
Physics.
Solid State Physics.
Spectroscopy and Microscopy.
Mathematical Methods in Physics.
Springer series in solid-state sciences