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

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.

18 pages, 3 figures

References in corpus (3)

• Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
• Matrix-valued Boltzmann Equation for the Hubbard Chain
• Matrix-valued Boltzmann equation for the non-integrable Hubbard chain

Cited by in corpus (12)

• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Hydrodynamics of weak integrability breaking
• Thermalization rates in the one dimensional Hubbard model with next-to-nearest neighbor hopping
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Tunable transport in the mass-imbalanced Fermi-Hubbard model
• Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory
• Matrix-valued Quantum Lattice Boltzmann Method
• Global well-posedness of the spatially homogeneous Hubbard-Boltzmann equation
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
• Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime
• Dynamics of the Bose-Hubbard Chain for Weak Interactions