Local constants of motion imply information propagation

摘要: Interacting quantum many-body systems are expected to thermalize, in the sense that evolution of local expectation values approaches a stationary value resembling thermal ensemble. This intuition is notably contradicted exhibiting localisation (MBL). In stark contrast non-interacting case Anderson localisation, entanglement states grows without limit over time, albeit slowly. this work, we establish novel link between information theory and notions condensed matter physics, capturing phenomenon Heisenberg picture. We show mere existence constants motion, often taken as defining property MBL, together with generic spectrum Hamiltonian, already sufficient rigorously prove propagation: these can be used send classical bit arbitrary distances, impact perturbation detected arbitrarily far away. counterintuitive result compatible further corroborates slow growth following global quenches MBL systems. perform detailed analysis quasi-local motion also they indeed construct efficient spectral tensor networks, recently suggested. Our results provide at same time model-independent picture propagation