Theoretical studies of the Mott transition in extended Hubbard models

The aim of the project is to understand the continuous phase transition between a Fermi liquid and a Mott insulator observed experimentally by John Saunders at Royal Holloway in a system of He-3 atoms deposited on a triangular lattice of He-4 atoms. This Mott transition takes place at a filling of 4/7 and is expected to be described by an extended Hubbard model on the triangular lattice. Miki will first study this model by using slave-particle mean-field theories, such as the Kotliar-Ruckenstein theory. As a next step we will analyse the effects of fluctuations of the gauge fields that arise from the slave-particle construction. As demonstrated by Senthil in the context of the Hubbard model with pure on-site repulsion, these fluctuations give rise to a critical non-Fermi liquid state that obeys the same scaling laws as Varma's marginal Fermi liquid. One important question is whether the additional breaking of translational symmetry, as seen in the helium system, can give rise to novel universal behaviour.