Reliability of the one-crossing approximation in describing the Mott transition

TL;DR

This study evaluates the one-crossing approximation's accuracy in modeling the Mott transition within dynamical mean field theory, revealing it captures the transition well but overestimates metallic correlations and shifts the insulator-metal transition.

Contribution

It provides a detailed comparison between OCA and quantum Monte Carlo methods for the Hubbard model, highlighting the strengths and limitations of OCA in describing the Mott transition.

Findings

OCA accurately predicts the phase diagram and metal-insulator transition point.

OCA overestimates metallic phase correlations and shifts the transition to higher U.

The insulator gap is underestimated due to spectral density moment inaccuracies.

Abstract

We assess the reliability of the one-crossing approximation (OCA) approach in quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in the conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds, and nanoscale systems. However, several recent studies in the framework of impurity models pointed out to serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behavior is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations for the system away from the particle-hole symmetric case are also presented and discussed.