After 50 years this remains a debated issue.
A number of distinct mechanisms for the transition have been proposed. These include those due to Brinkman and Rice (where the quasi-particle weight in the metallic phase approaches zero as the transition is approached), Hubbard (where vanishing of the charge gap occurs when the upper and lower Hubbard bands overlap), or Dynamical Mean-Field Theory (DMFT) which combines both these features.
My collaborators and I discuss an alternative mechanism in a paper that we just finished.
Holon-Doublon Binding as the Mechanism for the Mott transition
Peter Prelovsek, Jure Kokalj, Zala Lenarcic, and Ross H. McKenzie
We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system and a non-bipartite lattice a single holon-doublon (HD) pair exhibits a binding transition (e.g., on a face-centred cubic lattice), or a sharp crossover (e.g., on a triangular lattice) corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards non-polarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximation. Both approaches lead to a discontinuous transition away from the fully polarized system and give density correlations consistent with numerical results on a triangular lattice.
Two things I found (pleasantly) surprising in this study were:
-two "simple" analytical approaches (retraceable path approximation and a BCS-type variational wave function) seem to capture much of the essential physics.
-one can learn quite a lot by approaching the problem from the highly (spin) polarised limit.
We welcome comments and suggestions.