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

Quantum electrodynamics in 2+1 dimensions (QED₃) has been proposed as a critical field theory describing transitions of two-dimensional frustrated magnets and as the low-energy effective theory of a putative Dirac spin liquid. In this manuscript, we demonstrate that the intricate excitation spectrum close to criticality of the elementary but highly frustrated J₁-J₂ Heisenberg model on the triangular lattice is in one-to-one correspondence to explicitly constructed excitations from QED₃, including monopole and bilinear excitations. QED₃ is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, evidence for the emergence of a valence bond solid in the paramegnetic regime is presented. This suggests a scenario, where the critical point of a transition from the 120^? Néel order to a VBS is described by QED₃. Our results are obtained by constructing ansatz wave functions from a parton construction to exact eigenstates obtained and compared using large-scale Exact Diagonalization up to N=48 sites.