A multilevel method for many-electron Schrödinger equations based on the atomic cluster expansion. (English) Zbl 1537.81219
Summary: The atomic cluster expansion (ACE) [R. Drautz, Phys. Rev. B (3) 99, No. 1, Article ID 014104, 15 p. (2029; doi:10.1103/PhysRevB.99.014104)] yields a highly efficient and interpretable parameterization of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability of the ACE framework to the computation of many-electron wave functions. To that end, we develop a customized variational Monte Carlo algorithm that exploits the sparsity and hierarchical properties of ACE wave functions. We demonstrate the feasibility on a range of proof-of-concept applications to one-dimensional systems.
MSC:
| 81V45 | Atomic physics |
| 81V70 | Many-body theory; quantum Hall effect |
| 78A35 | Motion of charged particles |
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 05D40 | Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 65C05 | Monte Carlo methods |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 81-08 | Computational methods for problems pertaining to quantum theory |
Keywords:
many-electron Schrödinger equation; variational Monte Carlo; atomic cluster expansion; cascadic multilevel methodReferences:
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