Finite-temperature transport in finite-size Hubbard rings in the strong-coupling limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, $D(T,L),$ in the strongly correlated limit Ut for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t, we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=∞ case, the finite-temperature charge stiffness is finite for electronic densities n smaller than 1. These results are essentially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is ΔMH=U-4t, and we find that $D(T)$ is finite for $n<1,$ but is zero at half filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to Φᵉᶠᶠ=φ(Nₕ-Nd)/(Nd+Nₕ), and which is zero at half filling, with Nd and Nₕ being the number of doubly occupied and empty lattice sites, respectively. Further, for half filling, the current transported by any eigenstate of the system is zero and, therefore, $D(T)$ is also zero.