Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Abstract

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T > 0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T = 0 1D insulator the charge stiffness D(T ) vanishes for T > 0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U > 0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U = 0 and vanishes for U > 0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U = Uc = 0 for all finite temperatures T > 0. (At T = 0 such a transition is the quantum metal to Mott–Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finitetemperature charge transport properties of the 1D half-filled Hubbard model.