The electronic gas in the cuprate superconductors is believed to be
a strongly correlated
quantum system. To carry out an accurate calculation of models of these systems on large
size lattices is a very challenging problem. Thus, the process of figuring out which of
these models captures correctly the properties of these materials is very slow.
Exact diagonalization techniques face an exponentially growing size
Hilbert space with system size. This prohibits a convincing approach to the
thermodyncamic limit. The main bottleneck with stochastic techniques is that
we are dealing with fermions where the probability applitudes for
any given configuration does not have a well defined sign and thus
cannot be interpreted as probability distributions.
We have developed Monte Carlo techniques to study such systems.
These techniques are similar in spirit to the so-called Green's function
Monte Carlo method for fermions.
Using these techiques, we find that the effects of the strong short
bring the electonic system near an electronic phase separation instability which
is prevented by the long-range part of the Coulomb interaction.
The presense of this long-range interaction as well as the electron coupling to the
lattice seem to favor formation of stripes. We believe that the experimenally
seen stripes are a manifestation of the tendency of the system for
phase separation which is compromised in the formation of stripes.
There is a series of papers, including comments and replies which
clarify our beliefs.