Neural Network Quantum Monte Carlo Benchmark of Charge Symmetry Breaking in <i>A</i> = 3 − 7 Nuclei

We present a hybrid ab-initio framework combining Auxiliary Field Diffusion Monte Carlo with deep neural network optimized trial wavefunctions to benchmark Charge Symmetry Breaking effects in light nuclei with mass numbers from three to seven. Using a chiral inspired potential at next to next to leading order, we isolate the neutron-proton mass difference as the primary source of charge symmetry breaking. The neural network wavefunctions achieve a sixty-five percent reduction in Monte Carlo variance compared to traditional Jastrow-Slater ansätze, enabling a sub-keV precision calculation of the tritium-helium-three binding energy splitting. Our result is 0.7638±0.0008 MeV, which is dominated by the Coulomb interaction at 89.5% with a 10.5% contribution from the nuclear mass difference. We systematically map the charge symmetry breaking sensitivity across the mass chain, revealing a linear correlation between the isospin splitting and the three-nucleon low-energy constant c E with slope 1.52 ± 0.07 MeV. Charge radii for 3 H, 3 He, 4 He, 6 Li, and 7 Li are computed with less than one percent accuracy, and magnetic moments including meson exchange currents agree with experiment to within 0.3%. Our results demonstrate that machine learning optimized quantum Monte Carlo can achieve high precision in isospin-violating nuclear structure calculations.