Localization in the random XXZ quantum spin chain

Alexander Elgart, Abel Klein

Published 2022-10-26Version 1

We prove localization for the random XXZ quantum spin chain in the multi-cluster spectrum. The fractional moment method (FMM) is performed directly on the XXZ quantum spin chain Hamiltonian, using tools suitable for spin models. This requires significant modifications of the usual FMM method for random Schr\"odinger operators. In particular, the argument relies on a suitable replacement for the Green's function, the subject of the usual FMM. Performing the FMM on this new quantity requires a new set of ideas.