Using a fermionic ensemble of systems to determine excited states

We discuss a new numerical method for the determination of excited states o f a quantum system using a generalization of the Feynman-Kac formula. The m ethod relies on introducing an ensemble of non-interacting identical system s with a fermionic statistics imposed on the systems as a whole, and on det ermining the ground state of this fermionic ensemble by taking the long-tim e limit of the Euclidean kernel. Due to the exclusion principle, the ground state of an n-system ensemble is realized by the set of individual systems occupying successively the n lowest states, all of which can therefore be sampled in this way. To demonstrate how the method works, we consider a one -dimensional oscillator and a chain of harmonically coupled particles.