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First-quantized deep neural network techniques are developed for analyzingstrongly coupled fermionic systems on the lattice. Using a Slater-Jastrowinspired ansatz which exploits deep residual networks with convolutionalresidual blocks, we approximately determine the ground state of spinlessfermions on a square lattice with nearest-neighbor interactions. Theflexibility of the neural-network ansatz results in a high level of accuracywhen compared to exact diagonalization results on small systems, both forenergy and correlation functions. On large systems, we obtain accurateestimates of the boundaries between metallic and charge ordered phases as afunction of the interaction strength and the particle density.

Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states