  Electron correlation effects are particularly strong in the high temperature
superconducting materials. Devising an accurate description of these materials
has long been a challenge, with these strong correlation effects historically
being considered impossible or impractical to simulate computationally. Using
quantum Monte Carlo techniques, we have explicitly simulated electron
correlations in several cuprate materials from first principles. These
simulations accurately reproduce many important physical quantities about these
materials, including the interaction-induced gap and the superexchange coupling
between copper spins, with no additional parameters beyond fundamental
constants. We further investigate the dimensionless spin-lattice coupling
parameter in the parent materials, showing that it varies dramatically between
0.1 and 1.0 depending on the interlayer. This result indicates that the lattice
and magnetic degrees of freedom are not independent in these systems, which may
have ramifications for the origin of superconductivity.
