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Whether in the thermodynamic limit of lattice length $L\to \infty$, hole concentration $m^z_\eta =-2S^z_\eta / L =1-n_e \to 0$, nonzero temperature $T>0$, and $U/t>0$ the charge stiffness of the 1D Hubbard model with first neighbor transfer integral $t$ and on-site repulsion $U$ is finite or vanishe ...