Data of publication "Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems"

We study statistical properties of matrix elements entering the eigenstate thermalization hypoth-esis by studying the observables written in the energy eigenbasis and truncated to small micro-canonical windows. We put forward a picture, that below certain energy scale collective statisticalproperties of matrix elements exhibit emergent unitary symmetry. In particular, below this scale thespectrum of the microcanonically truncated operator exhibits universal behavior for which we intro-duce readily testable criteria. We support this picture by numerical simulations and demonstrateexistence of emergent unitary symmetry scale for all considered operators in chaotic many-bodyquantum systems. We discuss operator and system-size dependence of this energy scale and put ourfindings into context of previous works exploring emergence of random-matrix behavior in narrowenergy windows.