Dressing composite fermions with artificial intelligence

We present CF-Flow, composite-fermion (CF) wave-functions [1] augmented with backflow parameterized by symmetry-respecting neural networks. With CF-Flow, we use AI to understand how CFs are “dressed’’ as Landau level (LL) mixing is increased from zero. Our architecture uses orders-of-magnitude fewer parameters than recent Psiformer like models [2, 3], scales to larger systems (N ≥ 24 vs. N ≤ 12), and trains orders-of-magnitude faster. At fillings ν=1/3 and 2/5, energies from CF-Flow within the space of uniform states are nearly indistinguishable from fixed-phase diffusion Monte Carlo (fp-DMC) results [4] with the phase of CF wavefunctions. This agreement reveals an unexpected rigidity of the CF wave-function phase against LL mixing, explaining the long-standing success of the fixed-phase approximation. Furthermore, the symmetry-respecting architecture allows us to compute the ν=1/3 transport gap, which decays exponentially toward a finite value as LL mixing increases, never closing within the FQH phase.

[1] J. K. Jain, Composite-fermion approach for the fractional quantum Hall effect, Phys. Rev. Lett. 63, 199 (1989).

[2] Y. Teng, D. D. Dai, and L. Fu, Solving the fractional quantum Hall problem with self-attention neural network, Phys. Rev. B. 111, 205117 (2025).

[3] Y. Qian, T. Zhao, J. Zhang, T. Xiang, X. Li, and J. Chen, Describing Landau level mixing in fractional quantum Hall states with deep learning, Phys. Rev. Lett. 134, 176503 (2025).

[4] J. Zhao, Y. Zhang, and J. K. Jain, Crystallization in the fractional quantum hall regime induced by Landau-level mixing, Phys. Rev. Lett. 121, 116802 (2018).