On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
Year: 2020
Type: article
Abstract: 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 $$E_l$$ E l in all three methods due to unresolved states decay asymptotically exponentially like $$\exp (-(E_{n}-E_l)t)$$ 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 $$E_{n}-E_l$$ E n - E l . 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.
Source: The European Physical Journal A
Institutions: University of Bonn, Johannes Gutenberg University Mainz
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,160
Award: G5295195422
OpenAlex ID: W3018945988