Deep learning of topological phase transitions from entanglement aspects

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.

Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

“…ML has been successfully applied to a variety of physical problems, and vice versa, physics has inspired new directions to explore in understanding or improving ML techniques [1]. Among the most prominent and successful applications of ML in physics is the classification of phases in many body physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Of particular interest are unsupervised methods that require no or little prior information for labeling [2,3,[6][7][8]20].…”

Machine learning topological invariants of non-Hermitian systems

“…Machine learning, which lies at the core of the artificial intelligence and data science, has recently achieved huge success from industrial applications (especially in computer vision and natural language process) to fundamental researches in physics, cheminformatics and biology [1][2][3][4]. In physics, machine learning has shown its availability in experimental data analysis [5][6][7] and classification of phases of matter [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Among these applications, one of the most interesting problems is to extract the global properties of topological phases of matter from local inputs, such as the topological invariants that intrinsically nonlocal.…”

Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

“…ML has been successfully applied to a variety of physical problems, and vice versa, physics has inspired new directions to explore in understanding or improving ML techniques [1]. Among the most prominent and successful applications of ML in physics is the classification of phases in many body physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Of particular interest are unsupervised methods that require no or little prior information for labeling [2,3,[6][7][8]21].…”