Abstract
A recently developed Self-Healing Diffusion Monte Carlo Algorithm
[PRB {\bf 79}, 195117 ] is extended to the calculation of excited
states. The formalism is based on a excited-state fixed-node
approximation and the mixed estimator of the excited-state
probability density. The fixed-node ground state wave-functions of
inequivalent nodal pockets are found simultaneously using a recursive
approach. The decay of the wave-function into lower energy states is
prevented using two methods: i) The projection of the improved
trial-wave function into previously calculated eigenstates is
removed. ii) The reference energy for each nodal pocket is adjusted
in order to create a kink in the global fixed-node wave-function
which, when locally smoothed out, increases the volume of the higher
energy pockets at the expense of the lower energy ones until the
energies of every pocket become equal. This reference energy
method is designed to find nodal structures that are local minima
for arbitrary fluctuations of the nodes within a given nodal
topology. We demonstrate in a model system that the algorithm
converges to many-body eigenstates in bosonic-like and fermionic
cases.
