Quantum Monte Carlo with variable spins: Fixed-phase and fixed-node approximations

Abstract

We study several aspects of the recently introduced fixed-phase spinor diffusion Monte Carlo method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure calculations. We illustrate constructions of spinor-based wave functions with the full space-spin symmetry without assigning up or down spin labels to particular electrons, effectively “complexifying” even ordinary real-valued wave functions for Hamiltonians without spin terms. Interestingly, with proper choice of the simulation parameters and spin variables, such fixed-phase calculations enable one to reach also the fixed-node limit. The fixed-phase approximation has several desirable properties when compared to the fixed-node approximation. The fixed-phase solution provides a straightforward interpretation as the lowest bosonic state in a given effective potential generated by the many-body approximate phase, whereas nodal boundary conditions are defined through less intuitive and complicated hypersurfaces with one dimension less than the original configuration space. In addition, the divergences of the local energy and drift at real wave function nodes are smoothed out to lower dimensionality when the wave function is complexified, thus decreasing the variation of sampled quantities and eliminating artificial nodal domain issues that can occur in the fixed-node formalism. We illustrate some of these properties on calculations of selected first-row systems that recover the fixed-node results with quantitatively similar levels of the corresponding biases. At the same time, the fixed-phase approach opens new possibilities for more general trial wave functions with further opportunities for increasing accuracy in practical calculations.