SKM 2023 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 5: Correlated Electrons: Method Development

TT 5.13: Talk

Monday, March 27, 2023, 12:45–13:00, HSZ 204

Energy correlations of excited states in localization landscape theory — •Torsten Weber, Johannes Dieplinger, Christoph Forster, Lucas Resch, Ferdinand Evers, and Klaus Richter — Universität Regensburg, Regensburg, Deutschland

The localization landscape method, first described in [1], is a method that enables the prediction of the localization regions of eigenfunctions of a localized system. Additionally, the method gives a prediction of the energy of low-lying localized eigenfunctions by defining an effective potential from the landscape function [2]. This energy prediction, although providing good results for low energy eigenfunctions, ceases to work for higher energy states. Studying the method for a one-dimensional disordered system we observe a characteristic form of the ratio of the predicted eigenvalue by the landscape method and the actual eigenvalue for this region of the spectrum. We provide a possible explanation for this behaviour by extending the method leading to the energy prediction by including excited states of the effective potential. By harnessing the universal technique of quantifying excited states by counting nodes we observe a correspondence of the n-th excited states with the n-th repetition of a substructure of the characteristic behaviour described above. We go further to also find an analytic estimate for the structures.
[1] M. Filoche and S. Mayboroda, PNAS 109, 14761 (2012)
[2] D. N. Arnold et al., SIAM Journal on Scientific Computing, 41(1) (2019)