Topological invariant of periodic many body wavefunction from charge pumping simulation

Abstract

Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful computational framework for accessing these states, enabling the variational machine learning calculation of the system's ground state wavefunction. However, reliable computation of topological invariants remains an open challenge when the whole deterministic energy spectrum is not available. In this work, we introduce a robust approach to determining topological invariant based on simulating the charge pumping process, by monitoring the response of polarization upon flux insertion. By applying this method, we accurately extract the Chern numbers for Abelian fractional Chern insulators. Our approach also enables the first neural-network-wavefunction-based identification of anomalous composite Fermi liquid states. Our work resolves a key bottleneck in applying neural network wavefunctions to correlated topological matter, and the method proposed is also generally applicable to other many-body approaches, thereby opening up new avenues for future research in this field.