Linear-scaling fixed-node diffusion quantum Monte Carlo: Accounting for the nodal information in a density matrix-based scheme

Toward Linear Scaling Auxiliary-Field Quantum Monte Carlo with Local Natural Orbitals

We develop a local correlation variant of auxiliary-field quantum Monte Carlo (AFQMC) based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with the system size for a target accuracy, the method has linear scaling. Applying LNO-AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.

Preliminary Assessment of the First-Order Density Matrix in Quantum Monte Carlo from Density Matrix Theory

The trial wave function commonly used in the quantum Monte Carlo method consists of the product of up-spin and down-spin Slater determinants, allowing accurate calculations of multielectronic properties, although it is not antisymmetric under the exchange of electrons with opposite spins. An alternative description that overcomes these limitations using the Nth-order density matrix was already presented. This study introduces two new strategies based on the Dirac-Fock density matrix for QMC that still fully preserve antisymmetry and electron indistinguishability. Simulations are performed for the ground and excited states of He, Li, and Be showing that the present formulation and the conventional separation of spins are appropriate for a correct description of these systems, except for singlet excited states of the He and Be atoms, and that a part of the antisymmetry (antiparallel spins) can be neglected.