Spectroscopic signatures of hidden quantum critical points in one dimension

Topological phase transitions extend beyond the Ginzburg–Landau paradigm of spontaneous symmetry breaking (SSB) and long-range order. Such transitions can often be characterized by non-local order parameters that capture the system’s hidden order [1]. Here, we investigate a hidden quantum critical point that exhibits SSB in the absence of long-range order in the doped transverse-field Ising model. Using numerical and analytical approaches, we consistently identify experimentally viable signatures of the hidden order phase encoded in the dynamical spin structure factor: The interplay between spin and charge degrees of freedom leads to a doping-dependent shift of the gapless points of the Bogoliubov dispersion, which characterizes the excitation spectrum in the undoped limit. Our numerical results are supported by analytical arguments in squeezed space, which reveal a direct relation between the spin structure factor and a momentum-shifted charge structure factor.

[1] https://doi.org/10.48550/arXiv.2506.03146