Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
arXiv:2009.13585 · doi:10.1063/5.0031024
Abstract
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and algorithm of the method specialized for real materials, and present several recent developments. We give a systematic exposition of the key steps of AFQMC, closely tracking the framework of a modern software library we are developing. The building of a Monte Carlo Hamiltonian, projecting to the ground state, sampling two-body operators, phaseless approximation, and measuring ground state properties are discussed in details. An advanced implementation for multi-determinant trial wave functions is described which dramatically speeds up the algorithm and reduces the memory cost. We propose a self-consistent constraint for real materials, and discuss two flavors for its realization, either by coupling the AFQMC calculation to an effective independent-electron calculation, or via the natural orbitals of the computed one-body density matrix.
33 pages, 4 figures
References in corpus (17)
- QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
- Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
- Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
- On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules
- Direct comparison of many-body methods for realistic electronic Hamiltonians
- Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules
- Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
- Quantum Monte Carlo calculations in solids with downfolded Hamiltonians
- Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo
- The Stability, Energetics, and Magnetic States of Cobalt Adatoms on Graphene
- Predicting Ligand-Dissociation Energies of 3d Coordination Complexes with Auxiliary-Field Quantum Monte Carlo
- Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space
- Correlation effects in the ground state of trapped atomic Bose gases
- Stochastic Resolution-of-the-Identity Auxiliary-Field Quantum Monte Carlo: Scaling Reduction without Overhead
- Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics
- Metal-Insulator and Magnetic Phase Diagram of CaRuO from Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory
- A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo
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