Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems [1]. Here, we build over the results of Ref. [1] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to 12x12 on the triangular lattice.

[1] M. Hibat-Allah, M. Ganahl, L. E. Hayward, R. G. Melko, and J. Carrasquilla, "Recurrent neural network wave functions," Physical Review Research, Jun 2020.