  We analyze the high-temperature conductivity in one-dimensional integrable
models of interacting fermions: the t-V model (anisotropic Heisenberg spin
chain) and the Hubbard model, at half-filling in the regime corresponding to
insulating ground state. A microcanonical Lanczos method study for finite size
systems reveals anomalously large finite-size effects at low frequencies while
a frequency-moment analysis indicates a finite d.c. conductivity. This
phenomenon also appears in a prototype integrable quantum system of
impenetrable particles, representing a strong-coupling limit of both models. In
the thermodynamic limit, the two results could converge to a finite d.c.
conductivity rather than an ideal conductor or insulator scenario.
