Research data supporting 'Origin of exponential operator growth in Hilbert space'

This dataset contains the data obtained from computing the operator growth rates in model quantum systems, using the Lanczos algorithm. For more details, we refer the readers to the following publication: https://arxiv.org/pdf/2511.02800 The dataset is organised in terms of the figure number in the associated manuscript. Each folder contains text files with the simulation data stored in .txt format. The filenames contain the model name, parameters of the model (if applicable) and the simulation parameters (temperature, size of the system etc.). The code used to compute these data is available upon request. The following are the folders in the dataset: FIG1: Contains the Lanczos coefficients (bn, which measures the operator growth rate) for an operator obeying the Eigenstate Thermalisation Hypothesis (ETH) in a fictional system whose Hamiltonian is a given by a random-matrix ensemble (of size 300x300). The Lanczos coefficients are provided for the exponential, Gaussian and power-law decaying structure functions f_O as specified in the ETH. FIG2: Data containing the Lanczos coefficients for more realistic model potentials. FIG2a contains the data for operator O=x^100, where x is the position operator, compared with a hypothetical operator whose matrix elements are Gaussian decaying. FIG2b contains the Lanczos coefficients for the position operator in a quartic oscillator V(x)=x^4, and a hypothetical operator whose matrix elements are given by a WKB approximation to those of the position operator. FIG2c contains the Lanczos coefficients for the position operator in a particle in an infinite 1D box at different temperatures. FIG3: Data containing Lanczos coefficients for realistic physical systems in higher dimensions FIG3a contains Lanczos coefficients for the position operator in a stadium billiards and a rectangular box of similar dimensions at various temperatures. FIG3b contains the Lanczos coefficients for the spin-flip operator in an XXZ model with nearest-neighbour (NN) and next-to-nearest-neighbour (NNN) coupling. The inset contains the data to plot the structure function f_O in this system for the NN and NNN cases.