An efficient random-sampling method for calculating double occupancy of Gutzwiller wave function in single-band 1D and 2D lattices

We report a random-sampling method for computing the expectation value of physical quantities based on the Gutzwiler variational wave function. As the first application, we calculated the double occupancy, which is a critical quantity for understanding the correlation effects in many-body systems, for single-band 1D and 2D lattices. We demonstrated that the random-sampling scheme is more efficient than an existing Metropolis Monte-Carlo algorithm. For the 1D Hubbard model with only nearest-neighbour hopping, our results are almost identical to the exact analytic solution. We have also studied systems to which analytic solutions are not available, including the 1D lattices with next-nearest-neighbour hopping and 2D lattices. In addition, constraints on real-space configurations can be easily implemented in the current scheme to further improve the Gutzwiller wave function. As an example, we calculated the double occupancy for 1D Hubbard model by applying the constraint that all double-occupied sites are paired with an empty site. With enhanced correlation between double-occupied and empty sites, the constraint results in much improved ground-state energy for 1D Hubbard model with strong on-site repulsion.