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

TL;DR

This paper extends the auxiliary Hamiltonian approach to include non-local self-energies, enabling the treatment of spatially non-local correlations in many-body systems, demonstrated on the 1D Hubbard model.

Contribution

The authors generalize the auxiliary Hamiltonian method to handle non-local self-energies, overcoming previous limitations to local interactions.

Findings

The method can incorporate non-local correlation effects.

Application to 1D Hubbard model shows decay of Neel state.

Loss of time causality is a trade-off in the approach.

Abstract

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 Neel state in the weak-coupling regime, using the local and non-local second-order Born approximation.