Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator

The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( $p-h$) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when $p-h$ symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when $p-h$ symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is $p-h$ symmetry, whereas in its absence the gap diminishes with increasing disorder.