Spectral signatures of hidden order and hidden quantum critical points

Abstract

Hidden-order phases elude the conventional Ginzburg-Landau framework: although they spontaneously break symmetry, their order remains invisible to standard local two-point correlators. Instead, they are typically characterized by nonlocal (string) order parameters and are believed to underlie a range of exotic quantum states, such as symmetry-protected topological (SPT) phases. While hidden correlations have previously been detected through nonlocal observables in quantum gas microscope experiments, in realistic solid-state systems multipoint observables are typically inaccessible and the signatures of hidden order remain largely unexplored. In this work, we show that hidden order in doped spin chains can be directly probed through dynamical two-point response functions measurable by resonant inelastic X-ray scattering (RIXS) and neutron scattering. Focusing on a minimal model, we numerically identify clear spectral fingerprints of both the hidden-order phase, its associated hidden quantum critical point as well as a specific group of gapless SPT phases. Complementing our numerical results with analytical insights, we uncover the microscopic origin of these spectral signatures and demonstrate how they emerge from the interplay between spin and charge degrees of freedom. Together, our results establish spectroscopy as a practical probe of hidden order and gapless SPT phases and provide a unified understanding of the low-energy physics governing these unconventional quantum phases.