Dynamical Mean Field Theory equations on nearly real frequency axis

TL;DR

This paper introduces a method to solve DMFT equations on nearly real frequencies, revealing detailed structures of the metal-insulator transition at finite temperatures without the instabilities of traditional approaches.

Contribution

The authors develop a nearly real frequency approach for DMFT equations that captures fine structures of the MIT, avoiding analytic continuation issues present in conventional methods.

Findings

Reveals fine structures across the MIT at finite temperatures.

Shows an abrupt decrease in the quasi-particle peak at a critical U.

Finds no T* separating bad insulator from Mott insulator down to T=0.01.

Abstract

The Iterated Perturbation Theory (IPT) equations of the Dynamical Mean Field Theory (DMFT) for the half-filled Hubbard model, are solved on nearly real frequencies at various values of the Hubbard parameters $U$, to investigate the nature of metal-insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Pad\'e analytic continuation and reveals fine structures across the MIT at finite temperatures, which {\em can not be captured} by conventional methods for solving DMFT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is an abrupt decrease in the height of the quasi-particle (Kondo) peak at a critical value of $U_c$, to a non-zero but small bump which gradually suppresses as one moves deeper into the {\em bad} insulator regime. In contrast to Vollhardt and coworkers [J. Phys. Soc. Jpn. {\bf 74} (2005) 136], down to $T=0.01$ of the half-bandwidth we find no $T^*$ separating bad insulator from a true Mott insulator.