Electronic structure quantum Monte Carlo (original) (raw)

2000, Acta Physica Slovaca. Reviews and Tutorials

Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias. detailed analysis of theoretical ideas. Indeed, QMC is very much in the line of "it from bit" paradigm, alongside, for example, of substantional computational efforts in quantum chromodynamics which not only predict hadron masses but, at the same time, contribute to the validation of the fundamental theory. Similar simulations efforts exist in other areas of physics as well. Just a few decades ago it was almost unthinkable that one would be able to solve Schrödinger equation for hundreds of electrons in an explicit, many-body wave function framework. Today, such calculations are feasible using available computational resources. At the same time, much more remains to be done, of course, to make the methods more insightful, more efficient and their application less laborious. We hope this overview will contribute to the growing interest in this rapidly developing field of research.