Fermionic lattice models with first-quantized deep neural-network quantum states*

Variational simulation with Neural-Network quantum states (NQS) is a successful approach to solve challenging quantum spin and fermionic Hamiltonians. In fermionic systems NQS were used in the second quantized formalism, where the the fermionic Hamiltonian is mapped to a nonlocally interacting spin model.

In this talk I will describe first-quantized deep Neural-Network techniques for analyzing strongly coupled fermionic systems on the lattice. The advantage of this approach is that it preserves the locality of the physical interactions. Using a Slater-Jastrow inspired ansatz, which exploits deep residual networks with convolutional residual blocks, we approximate the ground state of spinless fermions on a square lattice with nearest-neighbor interactions and study its phase diagram. In large systems, we obtain accurate estimates of the boundaries between metallic and charge ordered phases as a function of the interaction strength and the particle density.