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.

arXiv comment11 pages, 8 figures. Close to the published version

References in corpus (69)

• Machine learning and the physical sciences
• Edge states and topological invariants of non-Hermitian systems
• Localization transitions in non-Hermitian quantum mechanics
• Machine learning phases of matter
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Learning phase transitions by confusion
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Discovering Phase Transitions with Unsupervised Learning
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Non-Hermitian Topological Invariants in Real Space
• Topological phase transition in non-Hermitian quasicrystals
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• New topological invariants in non-Hermitian systems
• Topological quantum matter with cold atoms
• Non-Hermitian Many-Body Localization
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Machine Learning Topological States
• Identifying topological order through unsupervised machine learning
• Quantum Loop Topography for Machine Learning
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Machine Learning Topological Invariants with Neural Networks
• The Machine Learning Landscape of Top Taggers
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Unsupervised machine learning and band topology
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Floquet Topological Phases of Non-Hermitian Systems
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Application of machine learning algorithms to the study of noise artifacts in gravitational-wave data
• Many-body approach to non-Hermitian physics in fermionic systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Machine learning of quantum phase transitions
• Unsupervised Manifold Clustering of Topological Phononics
• Non-Hermitian fractional quantum Hall states
• Deep Learning Topological Invariants of Band Insulators
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Real space mapping of topological invariants using artificial neural networks
• Automated discovery of characteristic features of phase transitions in many-body localization
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Machine learning topological phases in real space
• Interpreting machine learning of topological quantum phase transitions
• Unsupervised learning using topological data augmentation
• Quantum topology identification with deep neural networks and quantum walks
• Deep learning of topological phase transitions from entanglement aspects
• Machine learning non-Hermitian topological phases
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands

Cited by in corpus (21)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• 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
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way