Topological Order in Deep State

2025-12-01

AI Summary

This study addresses the fundamental challenge of identifying fractional quantum Chern insulator (FQCI) ground states and their topological order in strongly correlated topological matter—without prior symmetry assumptions or topological knowledge. We propose an attention-based deep variational wavefunction embedded within a variational Monte Carlo framework, enabling end-to-end discovery of FQCI ground states solely via energy minimization. Crucially, we introduce a real-space, single-wavefunction decomposition into many-body momentum configurations—bypassing symmetry constraints or post-hoc projection—to directly extract topological degeneracy in translationally invariant systems. This provides an efficient, unsupervised diagnostic for topological order. Numerical experiments across multiple filling factors accurately reproduce both ground-state energies and topological degeneracies of FQCIs, demonstrating the method’s efficacy and broad applicability to discovering strongly correlated topological phases.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Topic discovery and tracking

Abstract

Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however challenging owing to their strong-coupling nature that prevents conventional mean-field treatment. Here, we demonstrate that an attention-based deep neural network provides an expressive variational wavefunction that discovers fractional Chern insulator ground states purely through energy minimization without prior knowledge and achieves remarkable accuracy. We introduce an efficient method to extract ground state topological degeneracy -- a hallmark of topological order -- from a single optimized real-space wavefunction in translation-invariant systems by decomposing it into different many-body momentum sectors. Our results establish neural network variational Monte Carlo as a versatile tool for discovering strongly correlated topological phases.

Problem

• Discovering fractional Chern insulator ground states using attention-based neural networks
• Extracting topological degeneracy from a single optimized wavefunction in translation-invariant systems
• Establishing neural network variational Monte Carlo as a tool for strongly correlated topological phases

Innovation

• Attention-based neural network for variational wavefunction
• Extract topological degeneracy via momentum sector decomposition
• Neural network Monte Carlo discovers correlated topological phases