Abstract

The dimension of the Fock space of N electrons grows exponentially with N, and developing compact representations that can capture the most important correlations of many-body wave functions with polynomial resources is hence a necessity. Traditional representations (as for instance the Gutzwiller, the Jastrow, and the EPS ) directly reproduce a specific set of low-order correlations that are deemed important. Conversely, parameterisations based on the use of neural networks (NN) architectures have no clear physical interpretation, nonetheless they attracted a lot of attention for their formal systematic improvability. In my talk I will present “Gaussian process states” (GPS), a novel framework for the construction of many-body states based on Bayesian statistics and Gaussian process (GP) regression. Similarly to a NN representation, GPS possesses the “universal approximator” property but, differently from it, can be interpreted in terms of physically meaningful correlations. For instance, under specific limits a GPS is able to exactly reproduce Gutzwiller, Jastrow and EPS wave functions. I will introduce two numerical approaches to train a GPS : a “fragmentation” approach, and direct variational optimisation. Extensive benchmarking on the Fermionic Hubbard model in 1 and 2 spatial dimensions reveals the competitiveness of the GPS framework, which is found to achieve similar and often superior descriptions of correlated quantum problems than existing state-of-the-art approaches.