Showing papers by "Nuno M. R. Peres published in 1999"

Curvature of Levels and Charge Stiffness of One-Dimensional Spinless Fermions

Abstract: Combining the Bethe ansatz with a functional deviation expansion and using an asymptotic expansion of the Bethe ansatz equations, we compute the curvature of levels ${D}_{n}$ at any filling for the one-dimensional lattice spinless fermion model. We use these results to study the finite-temperature charge stiffness $D(T).$ We find that the curvature of the levels obeys, in general, the relation ${D}_{n}{=D}_{0}+\ensuremath{\delta}{D}_{n},$ where ${D}_{0}$ is the zero-temperature charge stiffness and $\ensuremath{\delta}{D}_{n}$ arises from excitations. Away from half-filling and for the low-energy (gapless) eigenstates, we find that the energy levels are, in general, flux dependent and, therefore, the system behaves as an ideal conductor, with $D(T)$ finite. We show that if gapped excitations are included the low-energy excitations feel an effective flux ${\ensuremath{\Phi}}^{\mathrm{eff}}$ which is different from what is usually expected. At half-filling, we prove, in the strong interacting limit and to order $1/V$ (V is the nearest-neighbor Coulomb interaction), that the energy levels are flux independent. This leads to a zero value for the curvature of levels ${D}_{n}$ and, as a consequence, to $D(T)=0,$ proving an earlier conjecture of Zotos and Prelov\ifmmode \check{s}\else \v{s}\fi{}ek [Phys. Rev. B 53, 983 (1996)].