Nearly deconfined spinon excitations in the square-lattice spin-1=2 Heisenberg antiferromagnet

Abstract

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 CuðDCOOÞ2 · 4D2O, where a broad spectral-weight continuum at wave vector q ¼ ðπ; 0Þ was interpreted as deconfined spinons, i.e., fractional excitations carrying half of the spin of a magnon. Our results at ðπ; 0Þ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at q ¼ ðπ=2; π=2Þ (as also seen experimentally). We further investigate the reasons for the small magnon weight at ðπ; 0Þ 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 ðπ; 0Þ in the experiments as nearly deconfined spinons—a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile ðπ; 0Þ-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 ðπ; 0Þ in the Heisenberg model, as well as the energy maximum and smaller continuum at ðπ=2; π=2Þ. It can also account for the rapid loss of the ðπ; 0Þ magnon with increasing Q and the remarkable persistence of a large magnon pole at q ¼ ðπ=2; π=2Þ even at the deconfined critical point. The fragility of the magnons close to ðπ; 0Þ 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 CuðDCOOÞ2 · 4D2O.