Name: Theoretical Methods for Strongly Correlated Electrons von David Senechal
SKU: 9780387008950
Price: 56.99 EUR
Availability: InStock

Theoretical Methods for Strongly Correlated Electrons Zusammenfassung

Theoretical Methods for Strongly Correlated Electrons David Senechal

Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions.

Inhaltsverzeichnis

Contents Series Preface Preface C. Bourbonnais, D. Senechal, A. Ruckenstein, and A.-M.S. Tremblay I Numerical Methods 1 Density Matrix Renormalization Karen Hallberg 1 Introduction 2 The Method 3 Applications 4 Other Extensions to DMRG 4.1 Classical Systems 4.2 Finite-Temperature DMRG 4.3 Phonons, Bosons and Disorder 4.4 Molecules and Quantum Chemistry 5 Dynamical Correlation Functions 5.1 Lanczos and Correction Vector Techniques 5.2 Moment Expansion 5.3 Finite Temperature Dynamics 6 Conclusions 7 References 2 Quantum Monte Carlo Methods for Strongly Correlated Electron Systems Shiwei Zhang 1 Introduction 2 Preliminaries 2.1 Starting Point of Quantum Monte Carlo (QMC) 2.2 Basics of Monte Carlo Techniques 2.3 Slater Determinant Space 2.4 Hubbard-Stratonovich Transformation 3 Standard Auxiliary-Field Quantum Monte Carlo 3.1 Ground-State Method 3.2 Finite-Temperature Method 4 Constrained Path Monte Carlo Methods-Ground-State and Finite-Temperature 4.1 Why and How Does the Sign Problem Occur? 4.2 The Constrained-Path Approximation 4.3 Ground-State Constrained Path Monte Carlo (CPMC) Method 4.4 Finite-Temperature Method 4.5 Additional Technical Issues 5 Illustrative Results 6 Summary 7 References A Brief Review of Con.guration-Space Methods A.1 Variational Monte Carlo A.2 Green's Function Monte Carlo (GFMC) II Lagrangian, Functional Integral, Renormalization Group, Conformal and Bosonization Methods Renormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite Temperature C. Bourbonnais, B. Guay and R. Wortis 1 Introduction 2 Scaling Ansatz for Fermions 2.1 One Dimension 2.2 Anisotropic Scaling and Crossover Phenomena 3 Free Fermion Limit 3.1 One Dimension 3.2 Interchain Coupling 4 The Kadano.-Wilson Renormalization Group 4.1 One-Dimensional Case 4.2 One-Loop Results 4.3 Two-Loop Results 4.4 Response Functions 5 Interchain Coupling: One-Particle Hopping 5.1 Interchain Pair Hopping and Long-Range Order 5.2 Long-Range Order in the Decon.ned Region 6 Kohn-Luttinger Mechanism in Quasi-One-Dimensional Metals 6.1 Generation of Interchain Pairing Channels 6.2 Possibility of Long-Range Order in the Interchain Pairing Channels 7 Summary and Concluding Remarks 8 References A One-Particle Self-Energy at the Two-Loop Level A.1 Backward and Forward Scattering Contributions A.2 Umklapp contribution 4 An Introduction to Bosonization D. Senechal 1 Quantum Field Theory in Condensed Matter 2 A Word on Conformal Symmetry 2.1 Scale and Conformal Invariance 2.2 Conformal Transformations 2.3 E.ect of Perturbations 2.4 The Central Charge 3 Interacting Electrons in One Dimension 3.1 Continuum Fields and Densities 3.2 Interactions 4 Bosonization: A Heuristic View 4.1 Why Is One-Dimension Special? 4.2 The Simple Boson 4.3 Bose Representation of the Fermion Field 5 Details of the Bosonization Procedure 5.1 Left and Right Boson Modes 5.2 Proof of the Bosonization Formulas: Vertex Operators 5.3 Bosonization of the Free-Electron Hamiltonian 5.4 Spectral Equivalence of Boson and Fermion 5.5 Case of Many Fermion Species: Klein Factors 5.6 Bosonization of Interactions 6 Exact Solution of the Tomonaga-Luttinger Model 6.1 Field and Velocity Renormalization 6.2 Left-Right Mixing 6.3 Correlation Functions 6.4 Spin or Charge Gap 7 Non-Abelian Bosonization 7.1 Symmetry Currents 7.2 Application to the Perturbed Tomonaga-Luttinger Model 8 Other Applications of Bosonization 8.1 The Spin- 12 Heisenberg Chain 8.2 Edge States in Quantum Hall Systems 8.3 And More

Zusätzliche Informationen

Sku

GOR013433083

ISBN 13

9780387008950

ISBN 10

0387008950

Titel

Theoretical Methods for Strongly Correlated Electrons David Senechal

Autor

David Senechal

Serien

CRM Series in Mathematical Physics

Zustand

Gebraucht - Sehr Gut

Bindung

Gebundene Ausgabe

Verlag

Springer-Verlag New York Inc.

Datum

20031001

Anzahl der Seiten

362

Preise

N/A

Begleitschreiben

Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.

Hinweis

Dies ist ein gebrauchtes Buch. Es wurde schon einmal gelesen und weist von der früheren Nutzung Gebrauchsspuren auf. Wir gehen davon aus, dass es im Großen und Ganzen in einem sehr guten Zustand ist. Sollten Sie jedoch nicht vollständig zufrieden sein, setzen Sie sich bitte mit uns in Verbindung.