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

TL;DR

This paper calculates the curvature of energy levels and charge stiffness in a one-dimensional spinless fermion model, revealing conditions under which the system behaves as a perfect conductor or insulator.

Contribution

It introduces a combined Bethe Ansatz and asymptotic expansion method to analyze level curvature and charge stiffness at any filling, including effects of gapped excitations.

Findings

Energy levels depend on flux away from half filling, indicating ideal conduction.

At half filling, energy levels are flux independent, leading to zero charge stiffness.

The results confirm the conjecture that charge stiffness vanishes at half filling in the strong interaction limit.

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+\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 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 \Phi^{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 consequence, to D(T)=0, proving an earlier conjecture of Zotos and Prelov\v{s}ek.