Hall Effect in the Hubbard Model: Low-Field Regime

The ac Hall conductivity in the Hubbard model has been calculated in the low-field large-correlation limit. It was found that the lowest order in the bandwidth for which the Hall conductivity is finite is second. The results of the second-order bandwidth calculation are then applied to a three-dimensional tight-binding model at $T=0\mathrm{}°$K with the result that the Hall conductivity vanishes just where the diagonal components of the conductivity tensor do—for a half-filled band. The Hall and drift mobilities are then calculated for this model for $T\ne 0°$K for the half-filled band. The drift mobility has an exponential temperature dependence, while the Hall mobility remains equal to zero to second order in bandwidth. The calculations assume that the frequency is greater than the bandwidth.