Lattice Regularized Diffusion Monte Carlo (LRDMC)

Lattice Regularized Diffusion Monte Carlo (LRDMC)#

Overview#

Lattice regularized diffusion Monte Carlo (LRDMC), initially proposed by Casula[1], is a projection technique that systematically improves a variational Ansatz. It is based on Green’s function Monte Carlo (GFMC)[2][3][4], filtering the ground-state wavefunction from a given trial wavefunction.

Practical points#

  1. No time-step error: unlike standard DMC, LRDMC does not rely on a Suzuki–Trotter decomposition. Instead, a systematic bias comes from the finite lattice spacing \(a\)[1]. To obtain an unbiased fixed-node (FN) energy, extrapolate results to \(a \to 0\) using several lattice spacings; the \(a \to 0\) extrapolation is typically smooth and well captured by low-order polynomial fits.

  2. Consistency with DMC: after removing the controllable \(a \to 0\) extrapolation, FN energies from LRDMC agree with standard DMC calculations[5].

  3. Multiple mesh sizes: LRDMC can introduce two mesh sizes (\(a\) and \(a'\)) so that regions near nuclei and valence regions are diffused appropriately[1][6]. This will be introduced into jQMC in future.

  4. Variational principle with ECPs: LRDMC retains the variational principle even in the presence of effective core potentials, analogous to the T-move treatment in standard DMC[1][7][8].

jQMC implements an LRDMC algorithm that maintains parallel efficiency for many walkers and many nodes via load-balancing across walkers[9].

For further algorithmic details, please see the textbook “Quantum Monte Carlo Approaches for Correlated Systems”[10].

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