Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited

TL;DR

This paper revisits the use of Iterated Perturbation Theory (IPT) within Dynamical Mean-Field Theory to analyze the two-particle correlations associated with the metal-insulator transition, providing analytical insights and comparisons with numerical methods.

Contribution

It introduces analytical expressions for two-particle vertices and the DMFT Jacobian using IPT, enabling detailed analysis with reduced computational cost.

Findings

Analytical formulas for response functions derived from IPT.

Comparison shows IPT results align with finite difference calculations.

Limitations include inability to interpret transition via Landau free energy.

Abstract

Recent advances in many-body physics have made it possible to study correlated electron systems at the two-particle level. In Dynamical Mean-Field theory, it has been shown that the metal-insulator phase diagram is closely related to the eigenstructure of the susceptibility. So far, this situation has been studied using accurate but numerically expensive solvers. Here, the Iterated Perturbation Theory (IPT) approximation is used instead. Its simplicity makes it possible to obtain analytical results for the two-particle vertex and the DMFT Jacobian. The limited computational cost also enables a detailed comparison of analytical expressions for the response functions to results obtained using finite differences. At the same time, the approximate nature of IPT precludes an interpretation of the metal-insulator transition in terms of a Landau free energy functional.