Thermal Transport for Many Body Tight-Binding Models

TL;DR

This paper examines the calculation of thermal transport coefficients in many-body tight-binding models, proposing an optimal Wannier basis for accurate current approximation and deriving expressions for the Hubbard model in infinite dimensions.

Contribution

It introduces a criterion for selecting an optimal Wannier basis to minimize current approximation errors and derives thermal current expressions for generalized Hubbard models.

Findings

Proposed a basis selection criterion for better transport calculations

Derived thermal current expressions for Hubbard models in infinite dimensions

Identified the contribution of long-range interactions to heat current

Abstract

We clarify some aspects of the calculation of the thermal transport coefficients. For a tight-binding Hamiltonian we discuss the approximate nature of the charge current and the thermal current obtained by Peierls substitution which is also identical to the equation of motion technique. We address the issue of choosing an appropriate basis for making the Peierls construction for transport calculations. We propose a criteria for finding an optimum Wannier basis where the difference between the exact current and the approximate one is minimum. Using the equations of motion we derive the thermal current for a generalized Hubbard model with density interaction. We identify a part which is the contribution from the long range interactions to the heat current. For the Hubbard model we derive expressions for the transport coefficients in the limit of infinite dimensions.