Evidence of universal spectral collapse at a marginal dynamical regime

Incoherent electronic states in strongly correlated materials are commonly attributed to disorder or material specific mechanisms. Here we show that incoherent spectra instead arise from self-generated dynamical disorder associated with competing fluctuations. In this regime, electron dynamics coupled to time-dependent scattering naturally produce a spectral function of the form rho (z) = exp(-z^2/4) Dnu (z), where z is a scaled energy and Dnu denotes the parabolic cylinder function. This form reflects a marginal dynamical regime characterized by non-Markovian temporal correlations. Applying this scaling function to angle resolved photoemission spectroscopy (ARPES) energy distribution curves from the cuprates Nd2-xCexCuO4 and Bi2Sr2CaCu2O8+delta, the Kagome metal CsCr3Sb5, and the double-layer nickelate La3Ni2O7, we find that incoherent spectra are quantitatively described by rho (z), differing only in non-universal amplitude and energy scales. After rescaling, the datasets collapse onto a single universal curve characterized by a fixed parabolic-cylinder order nu = -1/2. The observed spectral collapse indicates a fixed-point-like regime in which microscopic details such as lattice geometry, band structure, and chemical composition become irrelevant at low energies. These results establish a unified and quantitative framework for continuum-dominated ARPES spectra across diverse strongly correlated materials.