Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation

TL;DR

This paper investigates the conditions under which many-body theories yield unphysical solutions and proposes methods to identify and overcome these issues, providing insights applicable across weak and strong correlation regimes.

Contribution

It clarifies when and why unphysical solutions occur in many-body equations and offers a new approach for strong interactions, extending the understanding of Green's functions.

Findings

Unphysical solutions can be identified and avoided in many-body calculations.

Standard perturbation theory fails in strong-correlation regimes, requiring alternative methods.

The approach is validated with lithium fluoride's absorption spectrum and explains literature observations.

Abstract

Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of non-linear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green's function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green's function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.