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 Green's 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.

Federico Becca is a researcher at the National Research Council (CNR) working in the theoretical group of the Condensed Matter section of the International School for Advanced Studies (SISSA) in Trieste. His research focuses on different aspects of correlated systems on the lattice. His major scientific contributions include advances in frustrated magnets, superconductivity from strong electronic correlation, disordered fermionic and bosonic models, and Mott metal-insulator transitions.
Sandro Sorella is Professor of Condensed Matter Physics at the International School of Advanced Studies (SISSA) in Trieste. His focus is on the study of strongly-correlated electron systems by advanced numerical simulation techniques based on quantum Monte Carlo. He has developed novel Monte Carlo algorithms that are now widely used and considered state-of-the-art in the field.