publications

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journal articles

• [8] J. Phys.: Condens. Matter 33, 054002 (2021)

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

  JG, Ke Liu, and Lode Pollet

  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 D3h 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... more →

• [7] Phys. Rev. Research 3, 023016 (2021)

  Revealing the phase diagram of Kitaev materials by machine learning: Cooperation and competition between spin liquids

  Ke Liu, Nicolas Sadoune, Nihal Rao, JG, and Lode Pollet

  Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-broken phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the classical honeycomb Kitaev-Γ model in a magnetic field. Our machine learns the global phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic _S₃_ magnets, and two modulated _S₃ × Z₃_ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic orders already occur in the large-S limit, implying that critical parts of the... more →

• [6] Phys. Rev. B 100, 174408 (2019)

  Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning

  JG, Ke Liu, Ludovic D. C. Jaubert, Han Yan, Nic Shannon, and Lode Pollet

  Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine-learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter... more →

• [5] Phys. Rev. B 99, 104410 (2019)

  Learning multiple order parameters with interpretable machines

  Ke Liu, JG, and Lode Pollet

  Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that accommodate multiple phases of coexisting and competing orders, which are common in condensed matter physics, remain largely unexplored from a machine-learning perspective. In this paper, we investigate multiclassification of phases using support vector machines (SVMs) and apply a recently introduced kernel method for detecting hidden spin and orbital orders to learn multiple phases and their analytical order parameters. Our focus is on multipolar orders and their tensorial... more →

• [4] Phys. Rev. B 99, 060404(R) (2019)

  Probing hidden spin order with interpretable machine learning

  JG, Ke Liu, and Lode Pollet

  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... more →

• [3] SciPost Phys. Lect. Notes 2 (2018)

  Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron

  JG and Lode Pollet

  These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fröhlich polaron problem. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is... more →

• [2] Phys. Rev. E 97, 012706 (2018)

  Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries

  Ke Liu, JG, and Lode Pollet

  Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly non-trivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal and molecular systems. The classification of these phases has been known for a long time, however, their transitions to the disordered isotropic liquid phase remain largely unexplored, except for a few symmetries. In this work, we utilize a recently introduced non-Abelian gauge theory to explore the nature of the underlying nematic-isotropic transition for all three-dimensional polyhedral nematics. The gauge theory can readily be applied to nematic phases with an... more →

• [1] Phys. Rev. B 92, 245132 (2015)

  Finite-size effects in Luther-Emery phases of Holstein and Hubbard models

  JG, S. Hesselmann, S. Wessel, F. F. Assaad, and M. Hohenadler

  The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave (CDW) order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin gap significantly complicates finite-size numerical studies, and explains inconsistent previous results for Luttinger... more →

theses