Diffusion constants from the recursion method

TL;DR

This paper demonstrates that a Lanczos coefficient-based method can accurately compute diffusion constants in quantum many-body systems, addressing a challenging problem in understanding transport behavior.

Contribution

It introduces and validates a scarcely used Lanczos coefficient approach for calculating diffusion coefficients in various quantum models.

Findings

Accurate diffusion constants obtained for spin chains and ladders.

Method effective for magnetization and energy transport.

Applicable to nonintegrable and mixed-field Ising models.

Abstract

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 Lanczos coefficients, and demonstrate that this strategy allows for the accurate calculation of diffusion coefficients 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.