Spectroscopic Feature of Quantum Many-Body Scar States

We study the dynamical correlations of nonintegrable systems with quantum many-body scar (QMBS) states generated by a ladder operator. The spectral function of the ladder operator has an exact $\delta$-function peak induced by the QMBS states. As a concrete example, we show that in the one-dimensional (1D) spin-$1$ Affleck-Kennedy-Lieb-Tasaki model, the spectral function of two-magnon excitations exhibits a characteristic bow-tie shape composed of a $\delta$-function resonance peak at momentum $k=\pi$ and a continuum spectrum elsewhere. The two-magnon excitations can be observed with the resonant inelastic X-ray scattering spectroscopy on quasi-1D nickelates and other spin-$1$ antiferromagnetic materials, thus it paves the way to detecting the (approximate) QMBS states in realistic materials.