Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects

Abstract

Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions for topological phases of matter at low dimensions either in a supervised or an unsupervised learning protocol with the assistance of quantum information related quantities. In this work, we adopt our previous ML procedures to study quantum phase transitions of magnetism systems such as the XY and XXZ spin chains by using spin-spin correlation functions as the input data. We find that our proposed approach not only maps out the phase diagrams with accurate phase boundaries, but also indicates some new features that have not observed before. In particular, we define so-called relevant correlation functions to some corresponding phases that can always distinguish between those and their neighbors. Based on the unsupervised learning protocol we proposed [Phys. Rev. B 104, 165108 (2021)], the reduced latent representations of the inputs combined with the clustering algorithm show the connectedness or disconnectedness between neighboring clusters (phases), just corresponding to the continuous or disrupt quantum phase transition, respectively.

arXiv comment18 pages, 21 figures

References in corpus (35)

• The density-matrix renormalization group in the age of matrix product states
• Machine learning phases of matter
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Machine learning quantum phases of matter beyond the fermion sign problem
• Recovering the number of clusters in data sets with noise features using feature rescaling factors
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Identifying topological order through unsupervised machine learning
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Detection of phase transition via convolutional neural network
• Unsupervised machine learning and band topology
• 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
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Machine learning of phase transitions in the percolation and XY models
• Unsupervised phase discovery with deep anomaly detection
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Machine learning of quantum phase transitions
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Unsupervised machine learning of topological phase transitions from experimental data
• Deep Learning Topological Invariants of Band Insulators
• Unsupervised identification of topological order using predictive models
• Real space mapping of topological invariants using artificial neural networks
• Unsupervised machine learning of quantum phase transitions using diffusion maps
• Machine learning topological invariants of non-Hermitian systems
• Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions
• Quantum topology identification with deep neural networks and quantum walks
• Phase Detection with Neural Networks: Interpreting the Black Box
• Deep learning of topological phase transitions from entanglement aspects
• Unsupervised Learning Eigenstate Phases of Matter
• Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors

Cited by in corpus (2)

• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions