Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be notoriously difficult for a given microscopic model, even the seemingly simpler evaluation of transport coefficients in diffusive systems continues to be a hard task in practice. This fact has motivated the development and application of various sophisticated methods and is also the main issue of this paper. We particularly take a barely used strategy, which is based on the recursion method, and demonstrate that this strategy allows for accurate calculation of diffusion constants for different paradigmatic examples, including magnetization transport in nonintegrable spin-$1/2$ chains and ladders as well as energy transport in the mixed-field Ising model in one dimension.

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• Diffusion
• Quantum chaos
• Quantum statistical mechanics
• Quantum transport
• 1-dimensional spin chains
• Heisenberg model
• Ising model