Description
Springer Theoretical Methods For Strongly Correlated Electrons by David Senechal , Andre-Marie Tremblay , Claude Bourbonnais
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. ContentsSeries PrefacePreface C. Bourbonnais, D. Senechal, A. Ruckenstein, and A.-M.S. Tremblay I Numerical Methods1 Density Matrix RenormalizationKaren Hallberg1 Introduction 2 The Method 3 Applications 4 Other Extensions to DMRG4.1 Classical Systems4.2 Finite-Temperature DMRG4.3 Phonons, Bosons and Disorder4.4 Molecules and Quantum Chemistry 5 Dynamical Correlation Functions5.1 Lanczos and Correction Vector Techniques5.2 Moment Expansion5.3 Finite Temperature Dynamics 6 Conclusions 7 References 2 Quantum Monte Carlo Methods for Strongly Correlated Electron SystemsShiwei Zhang1 Introduction2 Preliminaries2.1 Starting Point of Quantum Monte Carlo (QMC)2.2 Basics of Monte Carlo Techniques2.3 Slater Determinant Space2.4 Hubbard-Stratonovich Transformation 3 Standard Auxiliary-Field Quantum Monte Carlo3.1 Ground-State Method3.2 Finite-Temperature Method 4 Constrained Path Monte Carlo Methods-Ground-State and Finite-Temperature4.1 Why and How Does the Sign Problem Occur?4.2 The Constrained-Path Approximation4.3 Ground-State Constrained Path Monte Carlo (CPMC) Method4.4 Finite-Temperature Method4.5 Additional Technical Issues 5 Illustrative Results 6 Summary 7 References A Brief Review of Con.guration-Space MethodsA.1 Variational Monte CarloA.2 Green's Function Monte Carlo (GFMC) II Lagrangian, Functional Integral,Renormalization Group, Conformal and Bosonization MethodsRenormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite TemperatureC. Bourbonnais, B. Guay and R. Wortis1 Introduction2 Scaling Ansatz for Fermions2.1 One Dimension2.2 Anisotropic Scaling and Crossover Phenomena 3 Free Fermion Limit3.1 One Dimension3.2 Interchain Coupling 4 The Kadano.-Wilson Renormalization Group4.1 One-Dimensional Case4.2 One-Loop Results4.3 Two-Loop Results4.4 Response Functions 5 Interchain Coupling: One-Particle Hopping5.1 Interchain Pair Hopping and Long-Range Order5.2 Long-Range Order in the Decon.ned Region 6 Kohn-Luttinger Mechanism in Quasi-One-Dimensional Metals6.1 Generation of Interchain Pairing Channels6.2 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 LevelA.1 Backward and Forward Scattering ContributionsA.2 Umklapp contribution 4 An Introduction to BosonizationD. Senechal1 Quantum Field Theory in Condensed Matter 2 A Word on Conformal Symmetry2.1 Scale and Conformal Invariance2.2 Conformal Transformations2.3 E.ect of Perturbations2.4 The Central Charge 3 Interacting Electrons in One Dimension3.1 Continuum Fields and Densities3.2 Interactions 4 Bosonization: A Heuristic View4.1 Why Is One-Dimension Special?4.2 The Simple Boson4.3 Bose Representation of the Fermion Field 5 Details of the Bosonization Procedure5.1 Left and Right Boson Modes5.2 Proof of the Bosonization Formulas: Vertex Operators5.3 Bosonization of the Free-Electron Hamiltonian5.4 Spectral Equivalence of Boson and Fermion5.5 Case of Many Fermion Species: Klein Factors5.6 Bosonization of Interactions 6 Exact Solution of the Tomonaga-Luttinger Model6.1 Field and Velocity Renormalization6.2 Left-Right Mixing 6.3 Correlation Functions6.4 Spin or Charge Gap 7 Non-Abelian Bosonization7.1 Symmetry Currents 7.2 Application to the Perturbed Tomonaga-Luttinger Model 8 Other Applications of Bosonization8.1 The Spin- 12 Heisenberg Chain8.2 Edge States in Quantum Hall Systems8.3 And More