Lanczos-Pascal Approach to Correlation Functions in Chaotic Quantum Systems

We suggest a method to compute approximations to temporal correlation functions of few-body observables in chaotic many-body systems in the thermodynamic limit based on the respective Lanczos coefficients. Given the knowledge of these Lanczos coefficients, the method is very cheap. Usually, accuracy increases with more Lanczos coefficients taken into account; however, we numerically find and analytically argue that the convergence is rather quick if the Lanczos coefficients exhibit a smoothly increasing structure. For pertinent examples, we compare with data from dynamical typicality computations for large but finite systems and find good agreement if few Lanczos coefficients are taken into account. From the method, it is evident that in these cases the correlation functions are well described by a low number of damped oscillations.