Suppression of the chiral current with increasing interaction energy U and K / J . The solid lines are fits of a DMRG simulation of the ideal chiral current with the amplitude as a single free parameter, the shaded areas denote the 1 sigma confidence interval of the fits and the dashed lines are perturbative approximations using the effective spin-1/2 model, scaled to the same fit amplitude. The grey dotdashed trace indicates the non-interacting current from an ED simulation at the same amplitude as the lowest U / K measurement. The inset shows the fit amplitude as a function of U / K . The legend indicates the average U / K for each curve, with the uncertainty denoting the 1 sigma variation throughout the K / J range. Each data point is averaged over 60 repetitions and 14 ladders with 48 sites. In all plots, the error bars denote the s.e.m., and if not visible, are smaller than the marker size.