Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
Qin, Yan Qi
Meng, Zi Yang
Sandvik, Anders W.
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Citation (published version)Hui Shao, Yan Qi Qin, Sylvain Capponi, Stefano Chesi, Zi Yang Meng, Anders W Sandvik. 2017. "Nearly Deconfined Spinon Excitations in the Square-Lattice Spin-1/2 Heisenberg Antiferromagnet." Physical Review X, Volume 7, Issue 4, Vol. 7, Iss. 4, 041072. https://doi.org/10.1103/PhysRevX.7.041072
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⋅4D2O, 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⋅4D2O.
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