Mott Physics in Correlated Lattices

Abstract

This thesis follows the Mott metal–insulator transition of the half-filled Hubbard model from every useful vantage point. In the weak-interaction limit we derive simple expressions that capture the familiar Fermi-liquid behaviour, while in the strong-interaction limit we show how the model reduces to an antiferromagnetic spin-exchange problem. These two analytical cornerstones pin down the physics at either end of the phase diagram.

To connect the two regimes we turn to dynamical mean-field theory, treating the lattice as an infinitely connected Bethe network whose simple density of states keeps the calculations transparent yet still mimics real three-dimensional oxides with many nearest neighbours. The numerical results trace, in a single framework, the loss of coherent quasiparticles, the appearance of Hubbard side-bands and the opening of the insulating gap. The predicted spectra and critical interaction strength line up well with the classic Mott system V₂O₃.

In combination, the analytic limits and the intermediate-coupling solution provide a coherent, start-to-finish narrative of how a weak-coupling Slater metal turns into a strong-coupling Mott insulator, and they deliver a set of benchmark results for future, more elaborate many-body calculations.