Freiburg 2024 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 24: Poster II

Q 24.37: Poster

Dienstag, 12. März 2024, 17:00–19:00, KG I Foyer

Linear Prediction Algorithms to enhance Impurity Solvers for Dynamical Mean Field Theory — •Bastian Schindler — Goethe-Universität, Institut für Theoretische Physik, 60438 Frankfurt am Main, Germany — Arnold-Sommerfeld-Zentrum für Theoretische Physik, LMU München, Theresienstr. 37, 80333 München

In the poster based on my bachelors thesis an empirical study of different linear prediction algorithms (Yule-Walker, Burg, covariance, modified covariance) using various implementations in python is presented. These algorithms are based on an autoregressive process and are being tested on the Greens functions generated during four different dynamical mean field theory (DMFT) simulations. To evaluate real world performance the root mean squared error is computed on a test sample, which was excluded from the previous fitting process. The dependency of this error with respect to most of the important hyperparameters is analysed systematically. Spectrums implementation of the covariance method is found to perform superiorly on weakly oscillating functions, whereas the Burg method from the same package overall performs better on strongly oscillating functions. The discarded weight is found to be a good parameter to distinguish between the two cases. A Nelder-Mead optimization scheme to find the relevant hyperparameters is successfully implemented. As my current interest in my masters project (Bose-Hubbard model with disorder) revolves heavily around bosonic DMFT, the link to (B)DMFT will be emphasized more than in the original thesis.

Keywords: Numerical Methods; Dynamical Mean Field Theory; Linear Prediction; Many Body Quantum Physics