Approximating strongly correlated spin and fermion wavefunctions with correlator product states*

We describe correlator product states, a class of numerically efficient many-body wave functions to describe strongly correlated wave functions in any dimension. Correlator product states introduce direct correlations between physical degrees of freedom in a simple way, yet provide the flexibility to describe a wide variety of systems. Variational Monte Carlo calculations for the Heisenberg and spinless fermion Hubbard models demonstrate the promise of correlator product states for describing both two-dimensional and fermion correlations. In one dimension, correlator product states appear competitive with matrix product states for the same number of variational parameters.