Computational Many-Particle Physics (Lecture Notes in Physics, 739)

Part I Molecular Dynamics
1 Introduction to Molecular Dynamics
Ralf Schneider, Amit Raj Sharma, and Abha Rai
Basic Approach
Macroscopic Parameters
Inter-Atomic Potentials
Numerical Integration Techniques
Analysis of MD Runs
From Classical to Quantum-Mechanical MD
Ab Initio MD
Car-Parrinello Molecular Dynamics
Potential Energy Surface
Advanced Numerical Methods
References
2 Wigner Function Quantum Molecular Dynamics
V. S. Filinov, M. Bonitz, A. Filinov, and V. O. Golubnychiy
Quantum Distribution Functions
Semiclassical Molecular Dynamics
Quantum Dynamics
Time Correlation Functions in the Canonical Ensemble
Discussion
References
Part II Classical Monte Carlo
3 The Monte Carlo Method, an Introduction
Detlev Reiter
What is a Monte Carlo Calculation?
Random Number Generation
Integration by Monte Carlo
Summary
References
4 Monte Carlo Methods in Classical Statistical Physics
Wolfhard Janke
Introduction
Statistical Physics Primer
The Monte Carlo Method
Cluster Algorithms
Statistical Analysis of Monte Carlo Data
Reweighting Techniques
Finite-Size Scaling Analysis
Generalized Ensemble Methods
Concluding Remarks
References
5 The Monte Carlo Method for Particle Transport Problems
Detlev Reiter
Transport Problems and Stochastic Processes
The Transport Equation: Fredholm IntegralEquation of Second Kind
The Boltzmann Equation
The Linear Integral Equation for the Collision Density
Monte Carlo Solution
Some Special Sampling Techniques
An Illustrative Example
References
Part III Kinetic Modelling
6 The Particle-in-Cell Method
David Tskhakaya
General Remarks
Integration of Equations of Particle Motion
Plasma Source and Boundary Effects
Calculation of Plasma Parameters and FieldsActing on Particles
Solution of Maxwell's Equations
Particle Collisions
Final Remarks
References
7 Gyrokinetic and Gyrofluid Theory and Simulation of Magnetized Plasmas
Richard D. Sydora
Introduction
Single Particle Dynamics
Continuum Gyrokinetics
Gyrofluid Model
Gyrokinetic Particle Simulation Model
Gyrokinetic Particle Simulation Model Applications
Summary
References
Part IV Semiclassical Approaches
8 Boltzmann Transport in Condensed Matter
Franz Xaver Bronold
Boltzmann Equation for Quasiparticles
Techniques for the Solution of the Boltzmann Equation
Conclusions
References
9 Semiclassical Description of Quantum Many-Particle Dynamics in Strong Laser Fields
Thomas Fennel and Jörg Köhn
Semiclassical Many-Particle Dynamicsin Mean-Field Approximation
Semiclassical Ground State
Application to Simple-Metal Clusters
References
Part V Quantum Monte Carlo
10 World-line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons
F.F. Assaad and H.G. Evertz
Introduction
Discrete Imaginary Time World Linesfor the XXZ Spin Chain
World-Line Representations without Discretization Error
Loop Operator Representationof the Heisenberg Model
Spin-Phonon Simulations
Auxiliary Field Quantum Monte Carlo Methods
Numerical Stabilization Schemes for Lattice Models
The Hirsch-Fye Impurity Algorithm
Selected Applications of the Auxiliary Field Method
Conclusion
The Trotter Decomposition
The Hubbard-Stratonovich Decomposition
Slater Determinants and their Properties
References
11 Autocorrelations in Quantum Monte Carlo Simulations of Electron-Phonon Models
Martin Hohenadler and Thomas C. Lang
Introduction
Holstein Model
Numerical Methods
Problem of Autocorrelations
Origin of Autocorrelations and Principal Components
Conclusions
References
12 Diagrammatic Monte Carlo and Stochastic Optimization Methods for Complex Composite Objects in Macroscopic Baths
A. S. Mishchenko
Introduction
Physical Properties of Interest
The Diagrammatic Monte Carlo Method
Stochastic Optimization Method
Conclusions and Perspectives
References
13 Path Integral Monte Carlo Simulation of Charged Particles in Traps
Alexei Filinov, Jens Böning, and Michael Bonitz
Introduction
Idea of Path Integral Monte Carlo
Basic Numerical Issues of PIMC
PIMC for Degenerate Bose Systems
Discussion
References
Part VI Ab-Initio Methods in Physics and Chemistry
14 Ab-Initio Approach to the Many-Electron Problem
Alexander Quandt
Introduction
An Orbital Approach to Chemistry
Hartree-Fock Theory
Density Functional Theory
References
15 Ab-Initio Methods Applied to Structure Optimization and Microscopic Modelling
Alexander Quandt
Exploring Energy Hypersurfaces
Applied Theoretical Chemistry
Model Hamiltonians
Summary and Outlook
Links to Popular Ab Initio Packages
References
Part VII Effective Field Approaches
16 Dynamical Mean-Field Approximation and Cluster Methods for Correlated Electron Systems
Thomas Pruschke
Introduction
Mean-Field Theory for Correlated Electron Systems
Extending the DMFT: Effective Cluster Theories
Conclusions
References
17 Local Distribution Approach
Andreas Alvermann and Holger Fehske
Introduction
Applications of the LD Approach
Summary
References
Part VIII Iterative Methods for Sparse Eigenvalue Problems
18 Exact Diagonalization Techniques
Alexander Weiße and Holger Fehske
Basis Construction
Eigenstates of Sparse Matrices
References
19 Chebyshev Expansion Techniques
Alexander Weiße and Holger Fehske
Chebyshev Expansion and Kernel Polynomial Approximation
Applications of the Kernel Polynomial Method
KPM in Relation to other Numerical Approaches
References
Part IX The Density Matrix Renormalisation Group: Concepts and Applications
20 The Conceptual Background of Density-Matrix Renormalization
Ingo Peschel and Viktor Eisler
Introduction
Entangled States
Reduced Density Matrices
Solvable Models
Spectra
Entanglement Entropy
Matrix-Product States
Summary
References
21 Density-Matrix Renormalization Group Algorithms
Eric Jeckelmann
Introduction
Matrix-Product States and (Super-)Blocks
Numerical Renormalization Group
Infinite-System DMRG Algorithm
Finite-System DMRG Algorithm
Additive Quantum Numbers
Truncation Errors
Computational Cost and Optimization
Basic Extensions
References
22 Dynamical Density-Matrix Renormalization Group
Eric Jeckelmann and Holger Benthien
Introduction
Methods for Simple Discrete Spectra
Dynamical DMRG
Finite-Size Scaling
Momentum-Dependent Quantities
Application: Spectral Function of the Hubbard Model
References
23 Studying Time-Dependent Quantum Phenomenawith the Density-Matrix Renormalization Group
Reinhard M. Noack, Salvatore R. Manmana, Stefan Wessel, and Alejandro Muramatsu
Time Dependence in Interacting Quantum Systems
Sudden Quench of Interacting Fermions
Discussion
References
24 Applications of Quantum Information in the Density-Matrix Renormalization Group
Ö. Legeza , R.M. Noack , J. Sólyom , and L. Tincani
Basic Concepts of Quantum Information Theory
Entropic Analysis of Quantum Phase Transitions
Discussion and Outlook
References
25 Density-Matrix Renormalization Group for Transfer Matrices: Static and Dynamical Properties of 1D Quantum Systems at Finite Temperature
Stefan Glocke, Andreas Klümper, and Jesko Sirker
Introduction
Quantum Transfer Matrix Theory
The Method -- DMRG Algorithm for the QTM
An Example: The Spin-1/2 Heisenberg Chain with Staggered and Uniform Magnetic Fields
Impurity and Boundary Contributions
Real-Time Dynamics
References
Part X Concepts of High Performance Computing
26 Architecture and Performance Characteristics of Modern High Performance Computers
Georg Hager and Gerhard Wellein
Microprocessors
Parallel Computing
Conclusion and Outlook
References
27 Optimization Techniques for Modern High Performance Computers
Georg Hager and Gerhard Wellein
Optimizing Serial Code
Shared-Memory Parallelization
Conclusion and Outlook
References
Appendix: Abbreviations
Index