Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Abstract

Quantum electrodynamics in $2+1$ dimensions (QED${}_3$) 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 $J_1$-$J_2$ Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED${}_3$, in the quantum spin liquid regime. This includes a large manifold of explicitly constructed monopole and bilinear excitations of QED${}_3$, 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 an emergent valence bond solid (VBS), which suggests a scenario where only the critical point of a transition from the $120^{\circ }$ Néel order to a VBS is described by QED${}_3$. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to $N=48$ sites.

8 pages, 5 figures, including supplementary material

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