Many-body calculations of low energy eigenstates in magnetic and periodic systems with self healing diffusion Monte Carlo: steps beyond the fixed-phase

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.