https://doi.org/10.1140/epjp/s13360-022-02769-6
Regular Article
Study of many-body localization by principal component analysis
School of Science, Hangzhou Dianzi University, 310027, Hangzhou, China
Received:
3
March
2022
Accepted:
25
April
2022
Published online:
3
May
2022
We employ the unsupervised machine learning algorithm—principal component analysis (PCA)—to the study of many-body localization (MBL) in random spin systems. Using eigenvalue spectra as the training data, PCA identifies the higher components to be close to the Fourier modes of the eigenvalues, which is further confirmed by the power spectrum function S(k). Moreover, it is shown S(k) in the thermal phase follows a power law 
which reflects its chaotic nature for 
, where 
is related to the Thouless energy, while in MBL phase S(k) follows 
standing for a regular system. We also show S(k) is able to reveal the Griffiths regime near critical region by studying its evolution during thermal–MBL transition. Our work provides a typical example of machine learning motivated study on complex quantum systems.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
