Dynamical thermal response functions for strongly correlated one-dimensional systems

In this article we study the thermal response functions for two one-dimensional models, namely the Hubbard and spin-less fermion $t$-$V$ models. By exactly diagonalizing finite sized systems we calculate dynamical electrical, thermoelectrical, and thermal conductivities via the Kubo formalism. The thermopower (Seebeck coefficient), Lorenz number, and dimensionless figure of merit are then constructed which are quantities of great interest to the physics community both theoretically and experimentally. We also geometrically frustrate these systems and destroy integrability by the inclusion of a second neighbor hop. These frustrated systems are shown to have enhanced thermopower and Lorenz number at intermediate and low temperatures.