Machine learning topological invariants of non-Hermitian systems

Abstract

The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train neural networks to predict the winding of eigenvalues of four prototypical non-Hermitian Hamiltonians on the complex energy plane with nearly $100\%$ accuracy. Our demonstrations in the non-Hermitian Hatano-Nelson model, Su-Schrieffer-Heeger model and generalized Aubry-André-Harper model in one dimension, and two-dimensional Dirac fermion model with non-Hermitian terms show the capability of the neural networks in exploring topological invariants and the associated topological phase transitions and topological phase diagrams in non-Hermitian systems. Moreover, the neural networks trained by a small data set in the phase diagram can successfully predict topological invariants in untouched phase regions. Thus, our work paves the way to revealing non-Hermitian topology with the machine learning toolbox.

11 pages, 8 figures. Close to the published version

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• Non-Hermitian Topological Phases: Principles and Prospects
• Unsupervised Learning of Non-Hermitian Topological Phases
• Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials
• Efficient sorting of orbital-angular-momentum states with large topological charges and their unknown superpositions via machine learning
• Damping transition in an open generalized Aubry-André-Harper model
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Unsupervised identification of Floquet topological phase boundaries
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• 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
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Quaternion-based machine learning on topological quantum systems
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Machine learning topological energy braiding of non-Bloch bands
• Recent progress on disorder-induced topological phases
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