A Sum Rule for Thermal Conductivity and Dynamical Thermal Transport Coefficients in Condensed Matter -I

TL;DR

This paper derives a sum rule for dynamical thermal conductivity in condensed matter models, providing exact formulas and estimates for thermopower and related transport coefficients, with implications for high-frequency behavior and lattice effects.

Contribution

It introduces a new sum rule for thermal conductivity, presents exact formulas for chemical potential, and extends thermopower calculations beyond the Heikes Mott formula considering lattice topology.

Findings

Sum rule for dynamical thermal conductivity derived

Exact formulas for chemical potential at T=0 provided

Estimates for thermopower in correlated lattice models included

Abstract

We display an interesting sum rule for the dynamical thermal conductivity for many standard models of condensed matter in terms of the expectation of a thermal operator. We present the thermal operator for several model systems of current interest, which enable an evaluation of the sum rule and the Lorentz number, the thermo electric figure of merit as well as the thermopower at high frequencies. As a by product, we present exact formulae for the T=0 chemical potential $\mu(0)$ for charged many-body systems, including the Hubbard model, in terms of expectation values of extensive operators. Simple estimates are provided for the thermopower of an infinitely correlated band model on the triangular lattice, modeling the physics of the sodium cobalt oxide system. The present result goes beyond the Heikes Mott formula for the thermopower, and contains an additional transport correction that is sensitive to the lattice topology as well as the sign of hopping.