School of Physics Annual Report 1999

For many years certain materials, such as the oxides of transition metals and the cuprate superconductors, have resisted attempts to understand their electronic properties in terms of standard electron band theory. The strong electron correlations in these materials requires more complex analysis in terms of a many-body picture.
IN A CONTINUING project, we have used high order exact series expansion methods to study two popular lattice models of strongly correlated electrons, viz. the Hubbard model and the t-J model. The latter is a common starting point for theories which attempt to understand the physics of the high T_c cuprate superconductors. Recent work includes: a study of one and two-hole states in the t-J model on the square lattice. By using perturbation expansions up to 13^th order we obtain precise results for the dispersion curve for 1-hole excitations and for a bound 2-hole complex. In the large kinetic energy limit we find p-wave bound states favoured over the expected d-wave states, which we claim is a manifestation of the Kohn-Luttinger effect.	a similar study of the t-J model on a two-leg ladder structure, which occurs in the material SrCu₂O₃. This system is an insulator with a finite gap ("spin-gap") for magnetic excitations. We determine, among other things, the region of the phase diagram where 2-hole bound states are stable a study of the Hubbard model on a two-leg ladder. For U=0 this system undergoes a transition from a band insulator to a metal, as the bonding and antibonding bands begin to overlap. For U0 the "band insulator" phase persists but the metallic phase is driven into a "Mott-insulator" phase. There appears to be a sharp phase transition between these regions, which becomes a smooth crossover at large values of U Chris Hamer, Jaan Oitmaa, & Wei Hong Zheng
Dispersion curves for two-hole bound states in the t-J model on the square lattice.

Lattice models of strongly correlated electrons