The auxiliary Hamiltonian approach and its generalization to non-local self-energies

Progress in Non-equilibrium Green's Functions

Balzer, Karsten^1

Rechenzentrum, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse 4, Kiel

24118, Germany^1

关键词: Auxiliary systems;    Eigen decomposition;    Hamiltonian approach;    Noninteracting;    Second orders;    Self-consistency;    Singular values;    Weak-coupling regime;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/696/1/012001/pdf
DOI  :  10.1088/1742-6596/696/1/012001

来源: IOP

【 摘 要 】

The recently introduced auxiliary Hamiltonian approach [Balzer K and Eckstein M 2014 Phys. Rev. B 89 035148] maps the problem of solving the two-time Kadanoff-Baym equations onto a noninteracting auxiliary system with additional bath degrees of freedom. While the original paper restricts the discussion to spatially local self-energies, we show that there exists a rather straightforward generalization to treat also non-local correlation effects. The only drawback is the loss of time causality due to a combined singular value and eigen decomposition of the two-time self-energy, the application of which inhibits one to establish the self-consistency directly on the time step. For derivation and illustration of the method, we consider the Hubbard model in one dimension and study the decay of the Néel state in the weak-coupling regime, using the local and non-local second-order Born approximation.