  Deep learning methods have been shown to be effective in representing
ground-state wave functions of quantum many-body systems. Existing methods use
convolutional neural networks (CNNs) for square lattices due to their
image-like structures. For non-square lattices, existing method uses graph
neural network (GNN) in which structure information is not precisely captured,
thereby requiring additional hand-crafted sublattice encoding. In this work, we
propose lattice convolutions in which a set of proposed operations are used to
convert non-square lattices into grid-like augmented lattices on which regular
convolution can be applied. Based on the proposed lattice convolutions, we
design lattice convolutional networks (LCN) that use self-gating and attention
mechanisms. Experimental results show that our method achieves performance on
par or better than existing methods on spin 1/2 $J_1$-$J_2$ Heisenberg model
over the square, honeycomb, triangular, and kagome lattices while without using
hand-crafted encoding.
