Similarities and differences in flat-band models with randomness detected by machine learning

Since Anderson localization was proposed, disordered electron systems have been studied extensively. As a recent development, systems that have characteristic electronic structures in the clean limit have been actively studied. For example, the flat-band (FB) systems have attracted attention because of their characteristic behavior to disorder [1,2]. Besides, it has also been shown, from the technical point of view, that machine learning (ML) is a useful method for identifying characteristic real-space distributions of wavefunctions. In our previous work, we studied the phase classification of FB states of molecular orbital (MO) models by ML [3]. A MO model is a model constructed on the basis of a linear combination of atomic orbitals, and it is known that macroscopic degeneracy remains even in the presence of randomness [4,5,6].

Based on these backgrounds, in this presentation, we compare a MO model with another random FB model. Specifically, we report the results of the ML study for the FB states of a random MO model and a model in which random potentials are introduced into the conventional FB model. In particular, we elaborate on how the choice of training data affects the output. We discuss the similarities and differences between the above two FB models inferred from the results.

[1] M. Goda, et al., PRL 96, 126401 (2006).

[2] J. T. Chalker, et al., PRB 82, 104209 (2010).

[3] T. Kuroda, et al., JPSJ 91, 044703 (2022).

[4] Y. Hatsugai, et al., EPL 95 20003 (2011).

[5] T. Mizoguchi, et al., EPL 127 47001 (2019).

[6] Y. Hatsugai, Ann Phys 168453 (2021).