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A recently developed self-healing diffusion Monte Carlo algorithm  [PRB 79, 195117] is extended to the calculation of excited states. Theformalism is based on an excited-state fixed-node approximation and the mixedestimator of the excited-state probability density. The fixed-node ground statewave-functions of inequivalent nodal pockets are found simultaneously using arecursive approach. The decay of the wave-function into lower energy states isprevented using two methods: i) The projection of the improved trial-wavefunction into previously calculated eigenstates is removed. ii) The referenceenergy for each nodal pocket is adjusted in order to create a kink in theglobal fixed-node wave-function which, when locally smoothed out, increases thevolume of the higher energy pockets at the expense of the lower energy onesuntil the energies of every pocket become equal. This reference energy methodis designed to find nodal structures that are local minima for arbitraryfluctuations of the nodes within a given nodal topology. We demonstrate in amodel system that the algorithm converges to many-body eigenstates inbosonic-like and fermionic cases.

Systematic reduction of sign errors in many-body problems: generalization of self-healing diffusion Monte Carlo to excited states