Real space quantum Monte Carlo pair orbital wave functions for periodic systems: toward the thermodynamic limit

Electronic structure quantum Monte Carlo calculations with supercells and periodicity are often complicated by finite size biases that often make evaluations of expectation values at the thermodynamic limit difficult and costly. There are many strategies and corrections how to overcome these complications, for example, checking that the calculated states/excitations share a common limit, ie, the thermodynamic consistency. One of the outstanding issues is sampling of the Brillouin zone which can be sampled by twists, however, this coud run into a slow and uneven convergence especially for metals with complex Fermi surfaces. In order to address this problem we suggest a particular form of many-body trial wave functions that offer elimination of this finite size bias component using general framework of pair orbitals and BCS-like or pfaffian forms. The theory is completely general and it provides possibilities to describe excited states including excitons in gapped systems. It is generalized to pfaffians built from spinor pairs for systems with spin-orbit and other spin-dependent interactions. We also consider some of the practical issues such as construction of pair orbitals and their efficient evaluations in quantum Monte Carlo methods.