Abstract
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo,
Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009), Reboredo, {\it
ibid.} {\bf 80}, 125110 (2009)] is extended to study the ground
and excited states of magnetic and periodic systems. A recursive
optimization algorithm is derived from the time evolution of the
mixed probability density. The mixed probability density is given by
an ensemble of electronic configurations (walkers) with complex
weight. This complex weigh allows the amplitude of the fix-node wave
function to move away from the trial wave function phase. This novel
approach is both a generalization of SHDMC and the fixed-phase
approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\bf 71},
2777 (1993)]. When used recursively it improves simultaneously the
node and phase. The algorithm is demonstrated to converge to the
nearly exact solutions of model systems with periodic boundary
conditions or applied magnetic fields. The method is also applied to
obtain low energy excitations with magnetic field or periodic
boundary conditions. The potential applications of this new method
to study periodic, magnetic, and complex Hamiltonians are discussed.
