Fourier Neural Operators for Many Body Physics Simulations in 2-dimensional Lattices

Fourier neural operators (FNOs) have become a powerful method for solving physics problems, due to their ability to learn operators and simulate partial differential equations. Studies that predict wave packets scattering from potentials and the dynamics of 1D Heisenberg chains have demonstrated FNOs’ ability to be applied to quantum dynamics [1,2]. Here, we deploy FNOs to extend the simulation of 2D Fermi Hubbard model dynamics. Tensor networks have been a popular choice for simulating many body problems, due to their effective contraction methods for Matrix Product States (MPS) and well known algorithms such as TEBD. However, due to the inaccuracy of mapping 2D systems to a 1D MPS as well as the entanglement of the system rising with evolution time, calculations involving tensor networks are exponentially hard and intractable for long time scales. In this study, we show that training FNOs on short term observable dynamics generated from tensor networks can extend our capacity to predict their behavior for longer times. We expect such calculations to expand our understanding of how observables of interest behave in the 2D Fermi Hubbard model, such as single site densities and multi-particle correlators, leading to meaningful insights in condensed matter systems. 

[1] Phys. Rev. D 108, L101701

[2] arXiv:2409.03302