Conductivity in a symmetry-broken phase: Spinless fermions with 1/d corrections

The dynamic conductivity σ(ω) of strongly correlated electrons in a symmetry-broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry-broken phase is the charge density wave (CDW) with wave vector Q=(π,π,π${)}^{\mathrm{†}}$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e., an expansion in the inverse dimension 1/d is used. The finite dimensionality is accounted for by the inclusion of linear terms in 1/d and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the nonsymmetry-broken and in the symmetry-broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit T→0 due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity σ(ω) the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order 1/d lead to an excitonic resonance lying within the gap. © 1996 The American Physical Society.