Robust persistent current sign in half-filled Hubbard rings fromthe exact electron factorisation

The electronic vector potential arising from the exact electron factorisation of a many-body wavefunction provides a direct bridge between the full wavefunction and the observable current density, but its behaviour under strong electron correlations remains largely unexplored. We address this question by applying the discrete exact electron factorisation to half-filled Hubbard rings threaded by a magnetic flux, across the full range from the non-interacting limit to the strongly correlated Mott regime. Our central result is that the direction of the persistent current is completely robust against electron-electron interactions for all ring sizes studied (N = 2 through N = 7): the current flows in a fixed direction for fluxes in (0,π) and the opposite direction for fluxes in (π,2π), independent of interaction strength, while only the amplitude is renormalised. The geometric origin of this robustness is the behaviour of the Wilson-loop phase of the conditional amplitude under interactions: at zero interaction the phase is quantised to ±π/2 over the two flux intervals, at the symmetric point ϕ = π/2 it is pinned exactly to -π/2 for all interaction strengths, and away from this point it drifts smoothly with interaction strength but never crosses zero. These findings establish the robustness of the current direction as a universal feature of the half-filled Hubbard ring, provide an exact benchmark for approximate current-density functionals, and offer a clear, falsifiable signature for cold-atom and quantum-dot realisations of Hubbard rings, where the current direction should remain fixed as the interaction strength is tuned.