Measuring out quasi-local integrals of motion from entanglement

Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body localisation, a phenomenon in which interactions and disorder come together. Despite the existence of several numerical ways to compute them—and in the light of the observation that much of the phenomenology of many properties can be derived from them—it is not obvious how to directly measure aspects of them in real quantum simulations; in fact, hard experimental evidence is still missing. In this work, we propose a way to extract the real-space properties of such quasi-local integrals of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body localisation from non-equilibrium dynamics. We complement these findings with a rigorous entanglement bound and compute the relevant quantities using tensor networks. We demonstrate that the entanglement gives rise to a well-defined length scale that can be measured in experiments.