# SciPost Thesis Link

Title: | Investigation of hidden multipolar spin order in frustrated magnets using interpretable machine learning techniqes | |

Author: | Jonas Greitemann | |

As Contributor: | Jonas Greitemann | |

Type: | Ph.D. | |

Discipline: | Physics | |

Subject area: | Condensed Matter Physics - Computational | |

Approaches: | Theoretical, Computational | |

URL: | https://edoc.ub.uni-muenchen.de/25057/ | |

Degree granting institution: | Ludwig-Maximilians-Universität München | |

Supervisor(s): | Lode Pollet | |

Defense date: | 2019-10-15 |

### Abstract:

Frustration gives rise to a plethora of intricate phenomena, the most salient of which are spin liquids, both classical ones—such as the spin-ice phase which has been realized experimentally in rare-earth oxide pyrochlore materials—and their more elusive quantum counterparts. At low temperatures, classical frustrated spin systems may still order, despite their extensive ground-state degeneracy, due to the order-by-disorder phenomenon. The resulting orders are often of a multipolar type which defies conventional probes. Identifying and characterizing such “hidden” orders is thus a challenging endeavor. This thesis introduces a machine-learning framework for studying the phase diagram of classical frustrated spin models in an unbiased and automated way. The interpretability of the resulting classification was of paramount importance in the design of the method. It allows for the inference of both the order parameter tensors of the phases with broken symmetries as well as the constraints which are characteristic of classical spin liquids and signal their emergent gauge structure. On top of that, it establishes a hierarchical relationship among the various phases according to their degree of disorder. The framework is applied to three different models and spin configurations are harvested from classical Monte Carlo simulations of those. A gauge model is used to mimic the interactions between the mesogens of generalized nematics. These may possess arbitrary point group symmetry, resulting in benchmark models with a low-temperature phase that breaks the O(3) spin symmetry accordingly. In addition, two frustrated spin models are considered. The historically important case of the Heisenberg model on the kagome lattice gives rise to hidden triatic order which requires a description in terms of two tensors of different ranks; the machine is capable of finding both. Meanwhile, for the XXZ model on the pyrochlore lattice, the machine reconstructs the complex phase diagram which was only recently obtained and correctly identifies the spin nematic phase as well as three distinct types of classical spin liquids, including their crossovers. The method has the potential to accelerate the characterization of model Hamiltonians of frustrated magnets. It can scrutinize the whole parameter space at once and may thus help to identify interesting regimes, paving the way for the search of new orders and spin liquids.