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 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) originated from Block correlation matrices (BCMs), 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 indeed too compressed information 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.

5 pages, 4 figures

References in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Classification of topological insulators and superconductors in three spatial dimensions
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Colloquium: Topological Band Theory
• Machine learning phases of matter
• Calculation of reduced density matrices from correlation functions
• Exponential Protection of Zero Modes in Majorana Islands
• A high-bias, low-variance introduction to Machine Learning for physicists
• Learning phase transitions by confusion
• Reduced density matrices and entanglement entropy in free lattice models
• Discovering Phase Transitions with Unsupervised Learning
• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Density-Matrix Spectra of Solvable Fermionic Systems
• Identifying topological order through unsupervised machine learning
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entanglement entropy and the Berry phase in solid states
• Detection of phase transition via convolutional neural network
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Machine learning out-of-equilibrium phases of matter
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Entanglement topological invariants for one-dimensional topological superconductors

Cited by in corpus (15)

• Unsupervised phase discovery with deep anomaly detection
• Machine learning topological invariants of non-Hermitian systems
• Phase Detection with Neural Networks: Interpreting the Black Box
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Neural networks in quantum many-body physics: a hands-on tutorial
• Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
• Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects
• Machine learning of mirror skin effects in the presence of disorder
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Quaternion-based machine learning on topological quantum systems
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Benchmarking quantum tomography completeness and fidelity with machine learning
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way