Origin of absent nonlinear Drude-weight divergences

Clarify why the divergences of higher-order nonlinear Drude weights predicted by the low-energy effective field theory are absent in exact Bethe-ansatz calculations for the quarter-filled one-dimensional Hubbard model, including whether the corresponding Umklapp coupling vanishes, is too small to observe, or whether the perturbative effective-field-theory treatment fails for higher-order nonlinear responses.

Background

At quarter filling, bosonization predicts that symmetry-allowed four-electron Umklapp interactions generate nonlinear Drude weights whose finite-size scaling diverges when the order exceeds a threshold determined by the Tomonaga–Luttinger-liquid parameter. However, exact Bethe-ansatz calculations through sufficiently high orders instead show finite thermodynamic-limit values with leading corrections of order L^{-2}.

The paper rules out an accidental cancellation specific to zero magnetic flux by reporting that the absence of divergence persists at finite flux. It discusses several unresolved explanations: the relevant Umklapp coupling might vanish because of constraints or special Hubbard-model symmetries, it might be nonzero but too small to produce observable divergences at the studied sizes and orders, or the perturbative low-energy field-theory calculation might be inadequate for higher-order nonlinear responses. The same discrepancy is also observed in the quarter-filled spin-1/2 XXZ chain, suggesting that the issue may reflect a broader limitation of the effective description.