Abstract:
We obtain a modified version of the Onsager regression relation for the expectation values of
quantum-mechanical operators in pure quantum states of isolated many-body quantum systems.
We use the insights gained from this relation to show that high-temperature time correlation
functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schroedinger equation for
randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential
reduction of the computer memory requirement in comparison with the complete diagonalization.
We illustrate the method by numerically computing infinite-temperature correlation functions for
translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin
diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the
derivation of the modified regression relation and the justification of the computational method
are based on the notion of quantum typicality.