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

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^∘ 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.