Quantum Monte Carlo pair orbital wave functions for periodic systems towards the thermodynamical limit: ground states, excitations and spinors

We derive many-body single- and multi-reference wave functions for quantum Monte Carlo of periodic systems with an anti-symmetric portion that explicitly integrates over the Brillouin zone of one-particle Bloch states. The wave functions are BCS-like determinants for singlets and pfaffians for polarized states built with appropriate pair orbitals. This ab initio formalism is broadly applicable, eg, to description of quasi-particle band gaps, optical excitations and to systems with complicated Fermi surfaces. It generalizes to spin-dependent interactions using two-component spinor pairs.