Density of states near the Mott-Hubbard transition in the limit of large dimensions

TL;DR

This paper investigates the behavior of the density of states near the Mott-Hubbard transition at zero temperature in large dimensions, analyzing possible transition scenarios through skeleton expansion.

Contribution

It provides a detailed analysis of the transition scenarios and the density of states behavior near the critical Coulomb repulsion U_c in the large-dimensional limit.

Findings

Two consistent transition scenarios identified: discontinuous transition with spectral weight redistribution.

Transition at U=U_c can be a point where the system is neither a Fermi liquid nor an insulator.

Abstract

The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion U is investigated in the limit of large dimensions. The behavior of the density of states near the transition at U=U_c is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for U<U_c: (i) The Mott-Hubbard transition is "discontinuous" in the sense that in the density of states finite spectral weight is redistributed at U_c. (ii) The transition occurs via a point at U=U_c where the system is neither a Fermi liquid nor an insulator.