Using a Fermionic Ensemble of Systems to Determine Excited States

Details Using a Fermionic Ensemble of Systems to Determine Excited States Using a Fermionic Ensemble of Systems to Determine Excited States

2000-11-27

arxiv.org/abs/hep-lat/0011082v1

J.Phys.A34:3947-3956,2001

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, Latex + 4 eps figures

Scientific paper

10.1088/0305-4470/34/19/301

We discuss a new numerical method for the determination of excited states of a quantum system using a generalization of the Feynman-Kac formula. The method relies on introducing an ensemble of non-interacting identical systems with a fermionic statistics imposed on the systems as a whole, and on determining the ground state of this fermionic ensemble by taking the large time 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.

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