Finite-Temperature Transport in Finite-Size Hubbard Rings in the Strong-Coupling Limit

TL;DR

This paper investigates finite-temperature charge transport in strongly correlated Hubbard rings, revealing that charge stiffness is finite below half-filling but zero at half-filling, with results derived via Bethe ansatz and algebraic methods.

Contribution

It provides a detailed analysis of charge stiffness in finite-size Hubbard rings at strong coupling, using two independent approaches, and clarifies the behavior at different fillings.

Findings

Charge stiffness is finite for densities less than one.

At half-filling, the charge stiffness is zero.

The effective flux felt by holons is renormalized and zero at half-filling.

Abstract

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, 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=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially 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 \Delta_{MH}=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 \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h 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.