David Logan

Abstract:

We study the magnetic properties of a site-disordered Anderson-Hubbard model at half-filling on a simple cubic lattice, via a mapping of its low-frequency transverse spin excitations onto those of an effective underlying Heisenberg model with self-consistently determined exchange couplings. Exact in the strong-coupling limit, the mapping remains accurate over the dominant region of the phase plane where the ground state is a disordered antiferromagnet. The effect of disorder and interaction strength on the resultant exchange couplings is examined in detail, and rationalized microscopically. Frustration is found to occur, even within the antiferromagnetic phase, although the ground state is shown to be stable with respect to zero-point quantum spin fluctuations. To probe finite-temperature magnetic properties, an Onsager reaction-field approach to the effective Heisenberg model in the paramagnetic phase is employed. We focus on the effect of disorder on the Néel temperature and the nature of the thermal transition to the ordered phase.

Abstract:

Current understanding of the Mott transition in the infinite-dimensional Hubbard model is reviewed. It is argued that the problem remains open, but is likely to hinge on a proper understanding of the role of exhaustion.