Abstract
Quantum electrodynamics in dimensions () has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from , in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of , which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by . Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to sites.
- Received 19 May 2023
- Revised 20 September 2023
- Accepted 26 January 2024
DOI:https://doi.org/10.1103/PhysRevX.14.021010
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. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
ViewpointViewing a Quantum Spin Liquid through QED
Published 15 April 2024
A numerical investigation has revealed a surprising correspondence between a lattice spin model and a quantum field theory.
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Popular Summary
Quantum electrodynamics (QED) is the fundamental theory that describes the interactions between electrons and photons. Its success has led some to wonder if quantum field theories, like QED, can describe quasiparticles in a solid. These collective excitations include phonons, which describe lattice vibrations, and magnons, which are waves in a magnetic material but might also be of a more exotic nature. Here, we show that QED in two spatial dimensions can be observed in frustrated antiferromagnets.
An antiferromagnet is a material where neighboring electron spins in the crystal lattice would like to point in opposite directions. However, on certain geometries, such as a triangular lattice, it is impossible to have all neighboring spins align precisely the opposite way. This is called geometric frustration and can lead to strong disorder in the system.
This disorder is not featureless, however. In fact, we show that the quasiparticles of such a spin soup, known as a quantum spin liquid, are related one-to-one to excitations of QED. Importantly, even the elusive magnetic monopoles, among a wide variety of other particle-hole excitations, are observed.
The precise understanding of the spin-liquid state with magnetic monopoles as elementary excitations is a key step to discovering these exotic quasiparticles in antiferromagnetic materials. It is unlikely that the founders of QED would have predicted such a surprising emergence in condensed matter.
