Deep learning of topological phase transitions from entanglement aspects
Yuan-Hong Tsai, Meng-Zhe Yu, Yu-Hao Hsu, Ming-Chiang Chung
Abstract
The one-dimensional $p$-wave superconductor proposed by Kitaev has long been a classic example for understanding topological phase transitions through various methods, such as examining the Berry phase, edge states of open chains, and, in particular, aspects from quantum entanglement of ground states. In order to understand the amount of information carried in the entanglement-related quantities, here we study topological phase transitions of the model with emphasis of using the deep learning approach. We feed different quantities, including Majorana correlation matrices (MCMs), entanglement spectra (ES) or entanglement eigenvectors (EE) originating from Block correlation matrices, into the deep neural networks for training, and investigate which one could be the most useful input format in this approach. We find that ES is information that is too compressed compared to MCM or EE. MCM and EE can provide us abundant information to recognize not only the topological phase transitions in the model but also phases of matter with different $U$(1) gauges, which is not reachable by using ES only.