We present a recently developed formalism for computing certain dynamical transport coefficients for standard models of correlated matter, such as the Hubbard and the $t-J$ model. The case of the Hall constant in correlated matter is used to motivate the method of high frequency. This method is pointed out to be closer to DC results for models describing low energy properties after eliminating high energy degrees of freedom. Successful predictions of this method are also noted. The extension of this method is made to evaluate and estimate the Seebeck coefficient, the Lorentz number L, and the figure of merit $Z T$, in terms of novel equal time correlation functions. Along the way, we uncover a new sum rule for the dynamical thermal conductivity for many standard models, precisely analogous to the f-sum rule for the electrical conductivity.
The new formalism is first tested in simple settings, such as the Sommerfield model of non interacting electrons within the Boltzmann approach. Further, recent computational results are displayed for testing the frequency dependence of these variables in certain standard models. These include some new predictions made regarding triangular lattice systems, motivated by the sodium cobaltate $Na_{.68} Co O_2$. A simple model for diffusion and relaxation of heat and charge transport in metallic systems is constructed, where the physical meaning of the new operators introduced in this formalism becomes clear. In this model, novel response functions relating induced charge and energy fluctuations to an input AC power source, such as a pulsed laser is obtained. |