Dressing composite fermions with artificial intelligence

TL;DR

This paper introduces CF-Flow, a neural network-based framework that models dressed composite fermions in fractional quantum Hall states, achieving high accuracy and efficiency, and providing new insights into phase transitions under Landau-level mixing.

Contribution

We develop CF-Flow, a symmetry-preserving neural network approach that models dressed composite fermions, improving accuracy and scalability over existing methods in FQH state simulations.

Findings

CF-Flow achieves near DMC accuracy for ground-state energies.

CF-Flow scales to systems with over 26 electrons.

Transport gap at ν=1/3 decays exponentially, indicating a phase transition.

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) wavefunctions, which accurately describe FQH states as weakly interacting states of CFs at fillings $\nu = n/(2pn+1)$ 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 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-a framework we refer to as CF-Flow. CF-Flow achieves competitive accuracy with substantially greater computational efficiency and scales to systems of $\gtrsim 26$ electrons. At fillings $\nu = 1/3$ and $2/5$, as a function of Landau-level mixing strength, CF-Flow produces ground-state energies with low local-energy variance that are nearly indistinguishable from those obtained using the fixed-phase diffusion Monte Carlo (fp-DMC) method, even though the latter constrains the wavefunction 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 $\nu = 1/3$, where we find, unexpectedly, that it decays exponentially toward a finite value in the limit of large Landau-level mixing, suggesting a first-order transition from the FQH liquid to a non-FQH state.