Topological Order in Deep State
This work provides a versatile tool for discovering strongly correlated topological phases, which is significant for researchers in quantum physics and materials science, though it appears incremental as it builds on existing neural network variational Monte Carlo methods.
The authors tackled the challenge of theoretically studying strongly correlated topological quantum phases by using an attention-based deep neural network as a variational wavefunction to discover fractional Chern insulator ground states through energy minimization, achieving remarkable accuracy and efficiently extracting topological degeneracy from a single optimized wavefunction.
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.