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arXiv:1805.05961 · Nature Physics

Identifying topological order through unsupervised machine learning

Joaquin F. Rodriguez-Nieva, Mathias S. Scheurer

Published May 6, 2019• 295 citations
arXivHTMLPDF
DOI
10.1038/s41567-019-0512-x

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In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool in identifying topological order since topology does not always manifest in obvious physical ways (e.g., topological superconductivity) for its decisive confirmation. The problem, however, is that unsupervised learning is a difficult challenge, necessitating huge computing resources, which may not always work. In the current work, we combine unsupervised and supervised learning to establish that unlabeled (simulated) data in the Majorana splitting in realistic short disordered nanowires may enable not only a distinction between `topological' and `trivial', but also where their crossover happens in the relevant parameter space. This may be a useful tool in identifying topology in experimental Majorana nanowires.
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Abstract Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.