3-phases Confusion Learning

Abstract: The use of Neural Networks in quantum many-body theory has seen a formidable rise in recent years. Among the many possible applications, one surely is to make use of their pattern recognition power when dealing with the study of equilibrium phase diagram. Within this context, Learning by Confusion has emerged as an interesting, unbiased scheme. The idea behind it briefly consists in iteratively label numerical results in a random way and then train and test a Neural Network; while for a generic random labeling the Network displays low accuracy, the latter shall display a peak when data are divided into a correct, yet unknown way. Here, we propose a generalization of this confusion scheme for systems with more than two phases, for which it was originally proposed. Our construction simply relies on the use of a slightly different Neural Network: from a binary classificator we move to a ternary one, more suitable to detect systems exhibiting three phases. After introducing this construction, we test is onto the free and the interacting Kitaev chain and on the one-dimensional Extended Hubbard model, always finding results compatible with previous works. Our work opens the way to wider use of Learning by Confusion, showing once more the usefulness of Machine Learning to address quantum many-body problems.