Anomalous scaling of conductivity in integrable fermion systems

Abstract

We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the $t\text{\ensuremath{-}}V$ 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 dc 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 dc conductivity rather than an ideal conductor or insulator scenario.