Quantum Monte Carlo Approaches for Correlated Systems

Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Greens function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.

Part I. Introduction: 1. Correlated models and wave functions; Part II. Probability and Sampling: 2. Probability theory; 3. Monte Carlo sampling and Markov chains; 4. Langevin molecular dynamics; Part III. Variational Monte Carlo: 5. Variational Monte Carlo; 6. Optimization of variational wave functions; 7. Time-dependent variational Monte Carlo; Part IV. Projection Techniques: 8. Green's function Monte Carlo; 9. Reptation quantum Monte Carlo; 10. Fixed-node approximation; 11. Auxiliary field quantum Monte Carlo; Part V. Advanced Topics: 12. Realistic simulations on the continuum; Appendix. Pseudo-random numbers generated by computers; References; Index.