Variational framework for projector quantum Monte Carlo

Projector Quantum Monte Carlo (PQMC) holds pivotal significance in ground-state studies of fermion systems. However, it often faces challenges due to the sign problem, rendering it impractical for large systems. Recent efforts have aimed to combine PQMC with variational approaches by relaxing the trotterized imaginary time projection operators. While these approaches introduce bias in the simulations, they significantly alleviate the sign problem, with the advantage of controllable bias within the variational framework. In this study, we delve into the variational structure of the ansatz, enhancing its flexibility and expressiveness. Additionally, We developed a general framework of automatic differentiation for optimizing the energy in PQMC, ensuring numerical stability of derivatives and enabling more projection steps than previous methods. We rigorously tested this approach across several strongly correlated systems, and our results indicate a promising path toward approximating the ground state in these complex systems.