Dynamical spin excitations of the topological Haldane gapped phase in the S =1 Heisenberg antiferromagnetic chain with single-ion anisotropy

We study the dynamical spin excitations of the one-dimensional S =1 Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid, and its dynamical signatures are similar to a S =1 /2 Heisenberg antiferromagnetic chain. The broad continuum can be seen as a dynamical signature of spinons. We further identify that the elementary excitations are fractionalized spinons in the critical state.