Probing hidden spin order with interpretable machine learning

Abstract

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

6 pages, 5 figures (+ 3 pages, 1 figure, 1 table Supplemental Materials), published as PRB Rapid Communication (Editors' Suggestion)

References in corpus (48)

• Quantum Spin Liquid States
• Machine learning phases of matter
• Magnetic Pyrochlore Oxides
• Learning phase transitions by confusion
• Spin-lattice coupling in frustrated antiferromagnets
• Discovering Phase Transitions with Unsupervised Learning
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• The "Coulomb phase" in frustrated systems
• Machine learning quantum phases of matter beyond the fermion sign problem
• Spin Ice, Fractionalization and Topological Order
• Colloquium: Hidden Order, Superconductivity, and Magnetism -- The Unsolved Case of URu2Si2
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Nematic order in square lattice frustrated ferromagnets
• Machine Learning Topological States
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning Phases of Strongly Correlated Fermions
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Machine learning vortices at the Kosterlitz-Thouless transition
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Probing many-body localization with neural networks
• Machine learning for many-body physics: The case of the Anderson impurity model
• Kernel methods for interpretable machine learning of order parameters
• Orbital ordering and frustration of $p$-band Mott-insulators
• Tetrahedral Magnetic Order and the Metal-Insulator Transition in the Pyrochlore Lattice of Cd2Os2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Field induced transitions in a kagome antiferromagnet
• Updated Core Libraries of the ALPS Project
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Evidence of a bond-nematic phase in LiCuVO4
• Nuclear magnetic resonance signature of the spin-nematic phase in LiCuVO${}_4$ at high magnetic fields
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• Ground-state phase diagram of an anisotropic spin-$1/2$ model on the triangular lattice
• Magnetic behavior of volborthite Cu3V2O7(OH)2(H2O)2 determined by coupled trimers rather than frustrated chains
• Quadrupole Order in the Frustrated Pyrochlore Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Hidden multipolar orders of dipole-octupole doublets on a triangular lattice
• Generalized liquid crystals: giant fluctuations and the vestigial chiral order of $I$, $O$ and $T$ matter
• Classical Spin Nematic Transition in LiGa${}_{0.95}$In${}_{0.05}$Cr${}_4$O${}_8$
• Classification of point-group-symmetric orientational ordering tensors
• Strong Orientational Coordinates and Orientational Order Parameters For Symmetric Objects
• Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries

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