Abstract
Interacting quantum many-body systems are expected to thermalize, in the sense that the evolution of local expectation values approaches a stationary value resembling a thermal ensemble. This intuition is notably contradicted in systems exhibiting many-body localisation (MBL). In stark contrast to the non-interacting case of Anderson localisation, the entanglement of states grows without limit over time, albeit slowly. In this work, we establish a novel link between quantum information theory and notions of condensed matter physics, capturing this phenomenon in the Heisenberg picture. We show that the mere existence of local constants of motion, often taken as the defining property of MBL, together with a generic spectrum of the Hamiltonian, is already sufficient to rigorously prove information propagation: these systems can be used to send a classical bit over arbitrary distances, in that the impact of a local perturbation can be detected arbitrarily far away. This counterintuitive result is compatible with and further corroborates the intuition of a slow entanglement growth following global quenches in MBL systems. We perform a detailed perturbation analysis of quasi-local constants of motion and also show that they indeed can be used to construct efficient spectral tensor networks, as recently suggested. Our results provide a detailed and at the same time model-independent picture of information propagation in MBL systems.
Highlights
When driven out of equilibrium, interacting quantum many-body systems are usually expected to thermalize [1,2,3], in the sense that local expectation values can be described by thermal ensembles
Such an expected generic behaviour is prominently violated by manybody localized (MBL) systems [4, 5] that show a strong suppression of transport [6,7,8,9] and fail to serve as their own heat bath [10, 11]
We present a rigorous proof for information propagation in MBL systems, using remarkably few and innocent assumptions: only the existence of local constants of motions and a generic spectrum
Summary
When driven out of equilibrium, interacting quantum many-body systems are usually expected to thermalize [1,2,3], in the sense that local expectation values can be described by thermal ensembles. For this to be at all possible, local expectation values need to equilibrate to an apparent stationary state and energy has to be transported through the entire system Such an expected generic behaviour is prominently violated by manybody localized (MBL) systems [4, 5] that show a strong suppression of transport [6,7,8,9] and fail to serve as their own heat bath [10, 11]. It came as some surprise that this is no longer the case in the presence of interactions and that entanglement entropies very slowly grow without limit over time [7, 8, 26] These numerical findings indicate that information is allowed to propagate in these models, at least for the infinite energy states usually considered, in a sense made more precise subsequently. Our results are a considerable step forward in the quest to prove that information is allowed to propagate in generic quantum many-body systems, which so far has only been achieved in highly specific systems
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