Diagrammatic Determinantal methods: projective schemes and applications to the Hubbard-Holstein model

TL;DR

This paper extends diagrammatic determinantal algorithms to projective schemes and phonon inclusion, enabling efficient zero-temperature studies of Hubbard-Holstein models within dynamical mean field theory.

Contribution

It introduces a novel extension of the weak-coupling diagrammatic determinantal algorithm to projective schemes and phonon integration, enhancing zero-temperature analysis capabilities.

Findings

Efficient zero-temperature calculations for Hubbard and Hubbard-Holstein models.

Successful implementation of phonon effects via retarded density-density interactions.

Validation of the extended algorithms within dynamical mean field theory.

Abstract

We extend the weak-coupling diagrammatic determinantal algorithm to projective schemes as well as to the inclusion of phonon degrees of freedom. The projective approach provides a very efficient algorithm to access zero temperature properties. To implement phonons, we integrate them out in favor of a retarded density-density interaction and simulate the resulting purely electronic action with the weak-coupling diagrammatic determinantal algorithm. Both extensions are tested within the dynamical mean field approximation for the Hubbard and Hubbard-Holstein models.