Dressing Composite Fermions with Artificial Intelligence

Abstract

Recent variational studies have demonstrated that the strongly correlated ground states of the fractional quantum Hall (FQH) effect can be captured using machine learning approaches starting from no prior knowledge of the underlying physics. We introduce a complementary framework that instead starts from Jain's composite-fermion (CF) wave functions, which accurately describe FQH states as weakly interacting states of CFs at fillings ν = n / ( 2 p n + 1 ) in an idealized limit. As we move away from this idealized limit to one more in line with experimental reality, we expect CFs to become dressed much like the electrons of a noninteracting system, which are dressed by neutral excitations as the interaction is turned on adiabatically, as in Landau's Fermi-liquid theory. We model this dressing using a Feynman-Cohen-style backflow approach, implemented through symmetry-preserving neural networks, which we refer to as CF-Flow. CF-Flow achieves competitive accuracy with substantially greater computational efficiency and scales to systems of ≳ 26 electrons. At fillings ν = 1 / 3 and 2 / 5 , CF-Flow produces ground-state energies as functions of Landau-level mixing strength that are nearly indistinguishable from those obtained using the fixed-phase diffusion Monte Carlo (fp-DMC) method, with low local-energy standard deviations, even though the latter constrains the wave function phase to that of the lowest Landau level, thereby providing insight into why fp-DMC has been successful in giving an accurate quantitative account of several experiments. Finally, the symmetry-preserving architecture of CF-Flow enables access to excited states and computation of the transport gap at ν = 1 / 3 and ν = 2 / 5 . Within the FQH sectors studied, the extrapolated gap is well described by an exponential decrease with Landau-level mixing and approaches a finite value at large mixing strength.