Misleading convergence of the skeleton diagrammatic technique: when the correct solution can be found

TL;DR

This paper investigates the convergence behavior of the skeleton diagrammatic technique (SDT), revealing that misleading convergence can sometimes be corrected through analytic continuation, enabling accurate solutions in challenging regimes.

Contribution

It demonstrates that misleading SDT convergence can be addressed by a modified protocol using analytic continuation, expanding the applicability of SDT to complex regimes.

Findings

Misleading SDT convergence can be corrected with analytic continuation.

The approach is validated on the Hubbard atom and 2d Hubbard model.

Controlled accuracy achieved with diagrammatic Monte Carlo.

Abstract

Convergence of the self-consistent skeleton diagrammatic technique (SDT) -- in which the full Green's function is determined through summation of Feynman diagrams in terms of itself -- to the wrong answer has been associated with the existence of non-perturbative branches of the Luttinger-Ward functional. Although it has been possible to detect misleading convergence without the knowledge of the exact result, the SDT has remained inapplicable in the regimes where this happens. We show that misleading convergence does not always preclude recovering the exact solution. In addition to the established mechanism, convergence of the SDT to the wrong answer can stem from divergence of the inherent diagrammatic series, which allows us to recover the exact solution by a modified SDT protocol based on controlled analytic continuation. We illustrate this approach by its application to the analytically solvable (0+0)d Hubbard model, the Hubbard atom, and the 2d Hubbard model in a challenging strong-coupling regime, for which the SDT is solved with controlled accuracy by the diagrammatic Monte Carlo (DiagMC) technique.