Disordered Hubbard model in $d=\infty$

TL;DR

This paper studies how static disorder affects the infinite-dimensional Hubbard model, revealing a transition from a Fermi liquid metal to an incoherent metal and eventually to an insulator, with detailed analysis of spectral and transport properties.

Contribution

It introduces a combined approach of iterated perturbation theory and coherent potential approximation to analyze disorder effects in the Hubbard model.

Findings

Fermi liquid phase remains stable at low disorder

Disorder induces a non-FL metallic phase with incoherence

Large disorder causes a transition to Mott-Anderson insulator

Abstract

We investigate the effects of static, diagonal disorder in the $d=\infty$ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi liquid coherence, leading to an {\it incoherent} metallic non-FL state off half-filling. Finally, for large enough disorder, a {\it continuous} transition to the Mott-Anderson insulating phase occurs. The nature of the non-FL metallic phase, as well as the effects of the low energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.