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Résumé |
We provide a novel Neural Network architecture that can: i) output R-matrix for a
given quantum integrable spin chain, ii) search for an integrable Hamiltonian and
the corresponding R-matrix under assumptions of certain symmetries or other
restrictions, iii) explore the space of Hamiltonians around already learned models
and reconstruct the family of integrable spin chains which they belong to. The
neural network training is done by minimizing loss functions encoding Yang-Baxter
equation, regularity and other model-specific restrictions such as hermiticity.
Holomorphy is implemented via the choice of activation functions. We demonstrate
the work of our Neural Network on the two-dimensional spin chains of difference
form. In particular, we reconstruct the R-matrices for all 14 classes. We also
demonstrate its utility as an Explorer, scanning a certain subspace of
Hamiltonians and identifying integrable classes after clusterisation. The last
strategy can be used in future to carve out the map of integrable spin chains in
higher dimensions and in more general settings where no analytical methods are
available. Particularly, at the end of my talk, I will present the first results
regarding the exploration of new integrable three-dimensional spin chains. |
