Ordered ground state configurations of the asymmetric Wigner bilayer system -- revisited: an unsupervised clustering algorithm analysis

TL;DR

This study applies unsupervised machine learning techniques to re-analyze and refine the classification of ground state configurations in the asymmetric Wigner bilayer system, revealing new structures and improving understanding.

Contribution

It introduces a systematic, machine learning-based approach using PCA and k-means clustering to classify complex ground states, surpassing previous manual methods.

Findings

Identification of new ground state structures

Refinement of the phase diagram classification

Validation confirms the robustness of the new scheme

Abstract

We have re-analysed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [M. Antlanger \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 118002 (2016)], comprising roughly 60~000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out ``by hand'', we have used this time machine learning concepts, notably based on a principal component analysis and a $k$-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters) we were able to re-analyse these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, identifying thereby a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.