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arXiv:cond-mat/9804169 · Physical review. B, Condensed matter

Curvature of levels and charge stiffness of one-dimensional spinless fermions

Nuno M. R. Peres, Pedro D Sacramento, David K Campbell, J. M. P. Carmelo

Published Mar 15, 1999• 33 citations
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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)].

DOI
10.1103/physrevb.59.7382

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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 Dn{D}_{n}Dn​ at any filling for the one-dimensional lattice spinless fermion model. We use these results to study the finite-temperature charge stiffness D(T).D(T).D(T). We find that the curvature of the levels obeys, in general, the relation Dn=D0+\ensuremathδDn,{D}_{n}{=D}_{0}+\ensuremath{\delta}{D}_{n},Dn​=D0​+\ensuremathδDn​, where D0{D}_{0}D0​ is the zero-temperature charge stiffness and \ensuremathδDn\ensuremath{\delta}{D}_{n}\ensuremathδDn​ 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)D(T)D(T) finite. We show that if gapped excitations are included the low-energy excitations feel an effective flux \ensuremathΦeff{\ensuremath{\Phi}}^{\mathrm{eff}}\ensuremathΦeff which is different from what is usually expected. At half-filling, we prove, in the strong interacting limit and to order 1/V1/V1/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 Dn{D}_{n}Dn​ and, as a consequence, to D(T)=0,D(T)=0,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)].
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