https://doi.org/10.1140/epja/s10050-020-00205-w
Special Article - Tools for Experiment and Theory
On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
1
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, Bonn, Germany
2
PRISMA+ Cluster of Excellence and Institut für Kernphysik, University of Mainz, Johann-Joachim-Becher-Weg 45, Mainz, Germany
* e-mail: urbach@hiskp.uni-bonn.de
Received:
28
April
2020
Accepted:
16
July
2020
Published online:
17
August
2020
We discuss the relation of a variety of different methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony, the generalised pencil of function and the Gardner methods. All three former methods can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energy 
in all three methods due to unresolved states decay asymptotically exponentially like 
. Using synthetic data we show that these corrections behave as expected also in practice. We propose a novel combination of the generalised eigenvalue and the Prony method, denoted as GEVM/PGEVM, which helps to increase the energy gap 
. We illustrate its usage and performance using lattice QCD examples. The Gardner method on the other hand is found less applicable to realistic noisy data.
© The Author(s), 2020
