Combining the Bethe Ansatz with a functional deviation expansion and using anasymptotic expansion of the Bethe Ansatz equations, we compute the curvature oflevels D_n at any filling for the one-dimensional lattice spinless fermionmodel. We use these results to study the finite temperature charge stiffnessD(T). We find that the curvature of the levels obeys, in general, the relationD_n=D_0+\delta D_n, where D_0 is the zero-temperature charge stiffness and\delta D_n arises from excitations. Away from half filling and for thelow-energy (gapless) eigenstates, we find that the energy levels are, ingeneral, flux dependent and, therefore, the system behaves as an idealconductor, with D(T) finite. We show that if gapped excitations are includedthe low-energy excitations feel an effective flux \Phi^{eff} which is differentfrom what is usually expected. At half filling, we prove, in the stronginteracting limit and to order 1/V (V is the nearest-neighbor Coulombinteraction), that the energy levels are flux independent. This leads to a zerovalue for the curvature of levels D_n and, as consequence, to D(T)=0, provingan earlier conjecture of Zotos and Prelov\v{s}ek.
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