Self-consistency in the phonon space of the particle-phonon coupling model

TL;DR

This paper introduces a non-linear extension of the time blocking approximation within the particle-phonon coupling model, enhancing self-consistency in the phonon space and ensuring convergence of results.

Contribution

It presents a novel non-linear generalization of the TBA that extends self-consistency to the phonon space, improving model convergence.

Findings

Non-linear TBA achieves convergence with larger phonon spaces.

Extension of self-consistency principle improves model stability.

Numerical examples demonstrate improved results.

Abstract

In the paper the non-linear generalization of the time blocking approximation (TBA) is presented. The TBA is one of the versions of the extended random-phase approximation (RPA) developed within the Green-function method and the particle-phonon coupling model. In the generalized version of the TBA the self-consistency principle is extended onto the phonon space of the model. The numerical examples show that this non-linear version of the TBA leads to the convergence of the results with respect to enlarging the phonon space of the model.