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arXiv · 2004.10472

On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods

Matthias Fischer·Bartosz Kostrzewa·Johann Ostmeyer·Konstantin Ottnad·Martin Ueding·Carsten Urbach
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Abstract

We discuss the relation of three methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony and the generalised pencil of function methods. All three can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energy $E_l$ in all three methods due to unresolved states decay asymptotically exponentially like $\exp(-(E_{n}-E_l)t)$. 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 $E_{n}-E_l$. We illustrate its usage and performance using lattice QCD examples.

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Matthias Fischer, Bartosz Kostrzewa, Johann Ostmeyer, Konstantin Ottnad, Martin Ueding, Carsten Urbach. 2020-04-22. On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods. https://doi.org/10.1140/epja/s10050-020-00205-w

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