Local dynamics and detection of topology in spin-1 chains

Antiferromagnetic spin-1 chains host the celebrated symmetry-protected topological Haldane phase, whose spin-$1/2$ edge states were evidenced in bulk by, e.g., electron spin resonance (ESR). To fully reveal and manipulate the spin-$1/2$ degree of freedom, one may build on the recent success in assembling effective spin-1 antiferromagnetic chains from nanographene and porphyrin molecules, and on the nascent technique of combined ESR and scanning tunneling microscopy, which is able to measure the spin dynamics site by site with atomic real-space resolution. In this Letter, we combine exact diagonalization and density matrix renormalization group to investigate the local dynamic spin structure factor of the different phases of the bilinear-biquadratic Hamiltonian with single-ion anisotropy in the presence of an external magnetic field. We find that the signature of the Haldane phase is a low-energy peak created by singlet-triplet transitions in the edge-state manifold. We predict that the signature peak is experimentally observable, although for chains of length above $N=30$ its energy should be first tuned by application of an external magnetic field. We fully characterize the peak in real space and energy, and further show its robustness to weak anisotropy and a relevant range of temperatures.