Characterizing many-body localization via exact disorder-averaged quantum noise

Many-body localized (MBL) phases of disordered quantum many-particle systems have a number of unique properties, including failure to act as a thermal bath and protection of quantum coherence. Studying MBL is complicated by the effects of rare ergodic regions, necessitating large system sizes and averaging over many disorder configurations. Here, building on the Feynman-Vernon theory of quantum baths, we characterize the quantum noise that a disordered spin system exerts on its parts via an influence matrix (IM). In this approach, disorder averaging is implemented exactly, and the thermodynamic-limit IM obeys a self-consistency equation. Viewed as a wavefunction in the space of trajectories of an individual spin, the IM exhibits slow scaling of temporal entanglement in the MBL phase. This enables efficient matrix product states computations to obtain temporal correlations, providing a benchmark for quantum simulations of non-equilibrium matter. The IM quantum noise formulation provides an alternative starting point for novel rigorous studies of MBL.