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

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