Electrical conductivity in the strong‐coupling non‐half‐filled band Hubbard model

The chemical potential μ and the electrical dc conductivity σ in the one‐dimensional Hubbard model in the strong‐coupling region U ≫ t ( U intra‐atomic Coulomb energy, – t nearest‐neighbour hopping integral) are calculated as functions of temperature and electron density n . In the non‐half‐filled band case n ≠ 1 the Bari‐Kaplan approximation lim (σ/ t 2 ) is shown to yield an unphysical singularity in the dc conductivity at T = 0 which is connected with the discontinuity of the zero‐temperature chemical potential at n = 1. An improved calculation for n ≠ 1 going beyond the Bari‐Kaplan approximation (i.e. taking into account the band terms in μ and σ/ t 2 ) yields a finite zero‐temperature conductivity which is proportional to the first power in t . For small deviations from the half‐filled band case the conductivity as a function of increasing temperature subsequently shows a metal‐like behaviour, a semiconductor‐like behaviour, and a repeated decrease at high temperatures.