Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems

• URL: http://arxiv.org/abs/2206.07370v1
• Date: Wed, 15 Jun 2022 08:24:37 GMT
• Title: Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems
• Authors: Cong Fu, Xuan Zhang, Huixin Zhang, Hongyi Ling, Shenglong Xu, Shuiwang Ji
• Abstract summary: We propose lattice convolutions in which a set of proposed operations are used to convert non-square lattices into grid-like augmented lattices. Based on the proposed lattice convolutions, we design lattice convolutional networks (LCN) that use self-gating and attention mechanisms.
• Score: 33.82764380485598
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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