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Abstract: Quantum Monte Carlo QMC is an advanced simulation methodology for studiesof manybody quantum systems. In this review, we focus on the electronicstructure QMC, i.e., methods relevant for systems described by the electron-ionHamiltonians. Some of the key QMC achievements include direct treatment ofelectron correlation, accuracy in predicting energy differences and favorablescaling in the system size. Calculations of atoms, molecules, clusters andsolids have demonstrated QMC applicability to real systems with hundreds ofelectrons while providing 90-95% of the correlation energy and energydifferences typically within a few percent of experiments. Advances in accuracybeyond these limits are hampered by the so-called fixed-node approximationwhich is used to circumvent the notorious fermion sign problem. Many-body nodesof fermion states and their properties have therefore become one of theimportant topics for further progress in predictive power and efficiency of QMCcalculations. Some of our recent results on the wave function nodes and relatednodal domain topologies will be briefly reviewed. This includes analysis offew-electron systems and descriptions of exact and approximate nodes usingtransformations and projections of the highly-dimensional nodal hypersurfacesinto the 3D space. Studies of fermion nodes offer new insights into topologicalproperties of eigenstates such as explicit demonstrations that genericfermionic ground states exhibit the minimal number of two nodal domains.Recently proposed trial wave functions based on Pfaffians with pairing orbitalsare presented and their nodal properties are tested in calculations of firstrow atoms and molecules. Finally, backflow -dressed- coordinates are introducedas another possibility for capturing correlation effects and for decreasing thefixed-node bias.

Autor: Michal Bajdich, Lubos Mitas

Fuente: https://arxiv.org/

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