Nearly Deconfined Spinon Excitations in the Square-Lattice Spin-1 /2 Heisenberg Antiferromagnet

We study the spin-excitation spectrum (dynamic structure factor) of the spin-1 /2 square-lattice Heisenberg antiferromagnet and an extended model (the J -Q model) including four-spin interactions Q in addition to the Heisenberg exchange J . Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with quantum Monte Carlo simulations, we can treat the sharp (δ -function) contribution to the structure factor expected from spin-wave (magnon) excitations, in addition to resolving a continuum above the magnon energy. Spectra for the Heisenberg model are in excellent agreement with recent neutron-scattering experiments on Cu (DCOO )₂.4 D₂O , where a broad spectral-weight continuum at wave vector q =(π ,0 ) was interpreted as deconfined spinons, i.e., fractional excitations carrying half of the spin of a magnon. Our results at (π ,0 ) show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at q =(π /2 ,π /2 ) (as also seen experimentally). We further investigate the reasons for the small magnon weight at (π ,0 ) and the nature of the corresponding excitation by studying the evolution of the spectral functions in the J -Q model. Upon turning on the Q interaction, we observe a rapid reduction of the magnon weight to zero, well before the system undergoes a deconfined quantum phase transition into a nonmagnetic spontaneously dimerized state. Based on these results, we reinterpret the picture of deconfined spinons at (π ,0 ) in the experiments as nearly deconfined spinons—a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile (π ,0 )-magnon pole in the Heisenberg model and its depletion in the J -Q model, we introduce an effective model of the excitations in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy to the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model can reproduce the reduction of magnon weight and lowered excitation energy at (π ,0 ) in the Heisenberg model, as well as the energy maximum and smaller continuum at (π /2 ,π /2 ). It can also account for the rapid loss of the (π ,0 ) magnon with increasing Q and the remarkable persistence of a large magnon pole at q =(π /2 ,π /2 ) even at the deconfined critical point. The fragility of the magnons close to (π ,0 ) in the Heisenberg model suggests that various interactions that likely are important in many materials—e.g., longer-range pair exchange, ring exchange, and spin-phonon interactions—may also destroy these magnons and lead to even stronger spinon signatures than in Cu (DCOO )₂.4 D₂O .