A Projector Quantum Monte Carlo Method for non-linear wavefunctions (L. Schwarz)

While previously these non-linear wavefunctions have traditionally been used in the area of Variational Monte Carlo, we consider recent developments for the identification of deep-learning neural networks to optimize this Lagrangian, which can be written as a modification of the propagator for the wavefunction dynamics.

We demonstrate the capability of this approach with a Correlator Product State wavefunction, a form of Tensor Network State, and use it to find solutions to the strongly-correlated Hubbard model, as well as ab-initio systems, including a linear hydrogen chain and a fully periodic, ab-initio graphene sheet. The number of variables which can be simultaneously optimized greatly exceeds alternative formulations of Variational Monte Carlo, allowing for systematic improvability of the wavefunction flexibility towards exactness, whilst combining traditional Variational and Projector Quantum Monte Carlo approaches.