• Open Access

Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice

Nikita Astrakhantsev, Tom Westerhout, Apoorv Tiwari, Kenny Choo, Ao Chen, Mark H. Fischer, Giuseppe Carleo, and Titus Neupert
Phys. Rev. X 11, 041021 – Published 29 October 2021

Abstract

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a resonating-valence-bond-like, many-variable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4×43 and 4×33 spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. We consider the (λ,j2/j1) parameter space, with j2, j1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

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  • Received 3 February 2021
  • Revised 12 August 2021
  • Accepted 2 September 2021

DOI:https://doi.org/10.1103/PhysRevX.11.041021

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nikita Astrakhantsev1,*, Tom Westerhout2,†, Apoorv Tiwari1,3, Kenny Choo1, Ao Chen4, Mark H. Fischer1, Giuseppe Carleo5, and Titus Neupert1

  • 1Department of Physics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
  • 2Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, Netherlands
  • 3Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
  • 4Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland
  • 5Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

  • *nikita.astrakhantsev@physik.uzh.ch
  • tom.westerhout@ru.nl

Popular Summary

Quantum magnets are materials in which spins arranged in a crystal lattice interact with each other. At low temperature, these spins often assume some type of order, such as collinear ferromagnetic ordering. However, materials known as quantum spin liquids avoid such ordering even down to the lowest temperatures, retaining their quantum fluctuations. Such materials are highly sought after because of their potential applications in quantum computing. Promising candidates include materials in which the atoms are arranged in a so-called “pyrochlore lattice,” a 3D network of corner-sharing tetrahedra. Its most frustrated Heisenberg regime, where spins interact with only their nearest neighbors in a “very quantum” way, has been inaccessible to theoretical study to date, and whether this model can host a quantum spin liquid is not yet settled. Our work, contrary to many expectations, gives a negative answer.

We reach this conclusion from extensive numerical simulations based on novel ways to represent the complex quantum wave functions including deep convolutional neural networks. These techniques allow us to simulate previously inaccessible system sizes and find an ordered ground state in which spins bond pairwise into dimers (local crystals) rather than forming a liquid.

Beyond this concrete physical result, our work is the first application of neural network quantum states to solve 3D quantum many-body systems. Such systems are a frontier for numerical simulations, as previously existing techniques were better suited for lower dimensions. Our work, on the contrary, showcases a novel way of obtaining high-quality solutions of quantum problems in three dimensions.

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Vol. 11, Iss. 4 — October - December 2021

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