Lower Bounding Diffusion Constant by Local Conservation Laws

Marko Medenjak, Christoph Karrasch, Tomaz Prosen

Published 2017-02-15Version 1

We establish a lower bound on Green-Kubo diffusion constant using local and quasilocal integrals of motion. The lower bound is connected to the behavior of Drude weight in the vicinity of half-filling, or vanishing magnetization. We use this result to explicitly determine a lower bound on the high temperature diffusion constant in the anisotropic spin 1/2 Heisenberg chain for anisotropy parameter $\Delta \geq 1$, thus settling the question whether the transport is sub-diffusive or not.