  We investigate the feasibility of simulating different model Hamiltonians
used in high-temperature superconductivity. We briefly discuss the most common
models and then focus on the simulation of the so-called t-J-U Hamiltonian
using ultra-cold atoms in optical lattices. For this purpose, previous
simulation schemes to realize the spin interaction term J are extended. We
especially overcome the condition of a filling factor of exactly one, which
otherwise would restrict the phase of the simulated system to a Mott-insulator.
Using ultra-cold atoms in optical lattices allows simulation of the discussed
models for a very wide range of parameters. The time needed to simulate the
Hamiltonian is estimated and the accuracy of the simulation process is
numerically investigated for small systems.
