Efficient representation of fully many-body localized systems using tensor networks (Dr. T. Wahl)

This makes tensor network states ideally suited to represent such fully many-body localized systems. Building on the ansatz proposed in Phys. Rev. B 94, 041116(R) (2016), I will present a tensor network that is able to capture the full set of eigenstates of such MBL systems efficiently: For a given system size, local observables can be approximated with an error that decreases as an inverse polynomial of the computational cost, which is an exponential improvement over the previous ansatz. If the system size is increased, the computational cost needs to grow only linearly with the system size in order to keep the accuracy fixed. The technique turns out to be highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the dynamical phase transition. Finally, the power of the technique is demonstrated on systems of 72 sites, where clear signatures of the phase transition can be seen.