Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure

Abstract

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo calculations (AFQMC). Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides increasing savings as the number of k points is increased, which is important in enabling calculations that approach the thermodynamic limit. The extension to non-Abelian symmetries is briefly discussed.

13 pages, 7 figures

References in corpus (9)

• Finite-size correction in many-body electronic structure calculations
• Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit
• Gaussian and plane-wave mixed density fitting for periodic systems
• Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
• 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
• 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
• An Auxiliary-Field Quantum Monte Carlo Study of the Chromium Dimer
• Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo

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