Quantum Electrodynamics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Abstract

Quantum electrodynamics in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> dimensions (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>QED</c:mi></c:mrow><c:mrow><c:mn>3</c:mn></c:mrow></c:msub></c:mrow></c:math>) 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>J</e:mi></e:mrow><e:mrow><e:mn>1</e:mn></e:mrow></e:msub><e:mtext>−</e:mtext><e:msub><e:mrow><e:mi>J</e:mi></e:mrow><e:mrow><e:mn>2</e:mn></e:mrow></e:msub></e:mrow></e:math> Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>QED</g:mi></g:mrow><g:mrow><g:mn>3</g:mn></g:mrow></g:msub></g:mrow></g:math>, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msub><i:mrow><i:mi>QED</i:mi></i:mrow><i:mrow><i:mn>3</i:mn></i:mrow></i:msub></i:mrow></i:math>, 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 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi>QED</k:mi></k:mrow><k:mrow><k:mn>3</k:mn></k:mrow></k:msub></k:mrow></k:math>. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>N</m:mi><m:mo>=</m:mo><m:mn>48</m:mn></m:math> sites. Published by the American Physical Society 2024

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