The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

TL;DR

This paper demonstrates how tensorial kernel support vector machines (TK-SVM) can effectively analyze and interpret complex phase structures and hidden orders in the classical kagome Heisenberg antiferromagnet, providing insights into its phase diagram and local constraints.

Contribution

The study introduces the application of TK-SVM to identify multipolar orders and phase hierarchy in a classical frustrated magnet, highlighting its interpretability and ability to uncover hidden physical features.

Findings

TK-SVM learns the finite-temperature phase diagram unsupervised.

Identifies tensorial quadrupolar and octupolar orders in the system.

Detects weak dipolar correlations at very low temperatures.

Abstract

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial $D_{3h}$ spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and a SVM bias parameter. For completeness we mention that the machine also picks up the leading $\sqrt{3} \times \sqrt{3}$ correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.