Derivation of a Matrix-valued Boltzmann Equation for the Hubbard Model

TL;DR

This paper derives a matrix-valued Boltzmann equation for the spin-1/2 Fermi-Hubbard model, providing detailed background for the previously stated kinetic equation used in weak interaction regimes.

Contribution

It offers a detailed derivation of the kinetic equation for the Hubbard model, filling a gap in the theoretical understanding of weakly interacting systems.

Findings

Derivation of the matrix-valued Boltzmann equation for the Hubbard model

Clarification of the background and assumptions used in the kinetic equation

Provides a foundation for future numerical and analytical studies

Abstract

For the spin-$\{1}{2}$ Fermi-Hubbard model we derive the kinetic equation valid for weak interactions by using time-dependent perturbation expansion up to second order. In recent theoretical and numerical studies the kinetic equation has been merely stated without further details. In this contribution we provide the required background material.