Robust Identification of Topological Phase Transition by Self-Supervised Machine Learning Approach

Abstract

We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of ultracold atoms. Different from the conventional supervised learning approach, where the predicted phase transition point is very sensitive to the training region and data labeling, our self-supervised learning approach identifies the phase transition point by the largest deviation of the predicted results from the known system parameters and by the highest confidence through a systematic shift of the training regions. We demonstrate the robust application of this approach results in various 1D and 2D exactly solvable models, using different input features (time-of-flight images, spatial correlation function or density-density correlation function). As a result, our self-supervised approach should be a very general and reliable method for many condensed matter or solid-state systems to observe new states of matters solely based on experimental measurements, even without a priori knowledge of the phase transition models.

arXiv comment13 pages and 7 figures

References in corpus (27)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Experimental realisation of the topological Haldane model
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Machine learning phases of matter
• Calculation of reduced density matrices from correlation functions
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Learning phase transitions by confusion
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Machine Learning Phases of Strongly Correlated Fermions
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Seeing topological order in time-of-flight measurements
• Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
• Measuring topology by dynamics: Chern number from linking number
• Entanglement entropy and the Berry phase in solid states
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Machine learning of phase transitions in the percolation and XY models
• Expansion of a quantum gas released from an optical lattice
• Machine learning of quantum phase transitions
• Unveiling phase transitions with machine learning
• Divergence of predictive model output as indication of phase transitions
• Electronic transport properties of topological insulator films and low dimensional superconductors

Cited by in corpus (5)

• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Quaternion-based machine learning on topological quantum systems
• Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems
• Classifying topological neural network quantum states via diffusion maps
• A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography