Machine learning vortices at the Kosterlitz-Thouless transition

Abstract

The authors extend the recent successful application of neural networks fordistinguishing phases of matter to the case of topologically driven phase transitions. They demonstrate that supervised networks correctly identify the Kosterlitz-Thouless transition in the two-dimensional classical XY model. However, their analysis suggests that a naive classification of phases is based on bulk features, rather than on detecting local topological defects. While they show that it is possible to fine-tune a network to recognize vortices, it generally remains a difficult task to detect topological defects without $a\phantom{\rule{0.333em}{0ex}}p\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i$ knowledge.