Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
Abstract
We study the dynamic spin structure factor of the spin-1/2 square-lattice Heisenberg antiferromagnet and of the J-Q model (with 4-spin interactions Q and Heisenberg exchange J). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp (δ-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)2·4D2O, where a broad spectral-weight continuum at q=(π,0) was interpreted as deconfined spinons. 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). Turning on Q, we observe a rapid reduction of the (π,0) magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret 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 in the Heisenberg model and its depletion in the J-Q model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the (π,0) and (π/2,π/2) features of the Heisenberg model. It can also account for the rapid loss of the (π,0) magnon with increasing Q and a remarkable persistence of a large magnon pole at q=(π/2,π/2) even at the deconfined critical point.