Simulations
of StronglyCorrelated Electrons University of California, Santa Barbara 
The discovery of high temperature superconductivity in 1986 and the subsequent proliferation of model systems and theoretical explanations made it clear that it would be useful to understand the actual properties of some manyelectron Hamiltonians. In the case of onedimensional systems, analytic solutions for a few particular Hamiltonians have provided important insights. However, in two or three dimensions we have few exact analytic results. One approach to this problem has been the development of numerical techniques aimed at obtaining controlled results for finite lattices. Some examples include Lancoz diagonalization, quantum Monte Carlo (QMC), stochastic series expansion (SSE) and density matrix renormalization group (DMRG) methods. 

