Quantum Monte Carlo Methods

Algorithms for Lattice Models

James Gubernatis, Naoki Kawashima, Philipp Werner

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN:
  9781107006423
• eBook ISBN:
  9781316484845
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Table of contents
• Preface
• Part I Monte Carlo basics
• Part II Finite temperature
• Part III Zero temperature
• Part IV Other topics
• Appendix A Alias method
• Appendix B Rejection method
• Appendix C Extended-ensemble methods
• Appendix D Loop/cluster algorithms: SU(N) model
• Appendix E Long-range interactions
• Appendix F Thouless’s theorem
• Appendix G Hubbard-Stratonovich transformations
• Appendix H Multi-electron propagator
• Appendix I Zero temperature determinant method
• Appendix J Anderson impurity model: chain representation
• Appendix K Anderson impurity model: action formulation
• Appendix L Continuous-time auxiliary-field algorithm
• Appendix M Continuous-time determinant algorithm
• Appendix N Correlated sampling
• Appendix O The Bryan algorithm
• References
• Index