In this work, we proposed a novel approach for identifying quantum phase transitions in one-dimensional quantum many-body systems using AutoEncoder (AE), an unsupervised machine learning technique, with minimal prior knowledge. The training of the AEs is done with reduced density matrix (RDM) data obtained by Exact Diagonalization (ED) across the entire range of the driving parameter and thus no prior knowledge of the phase diagram is required. With this method, we successfully detect the phase transitions in a wide range of models with multiple phase transitions of different types, including the topological and the Berezinskii-Kosterlitz-Thouless transitions by tracking the changes in the reconstruction loss of the AE. The learned representation of the AE is used to characterize the physical phenomena underlying different quantum phases. Our methodology demonstrates a new approach to studying quantum phase transitions with minimal knowledge, small amount of needed data, and produces compressed representations of the quantum states.
Validerad;2025;Nivå 2;2025-03-17 (u5);
Full text license: CC BY 4.0;
Funder: Research Grants Council ofHong Kong (CityU 11318722); National Natural Science Foundation of China (12204130); Shenzhen Start-Up Research Funds (HA11409065); City University of Hong Kong (9610438, 7005610, 9680320); HITSZ Start-Up Funds (X2022000);