Many-body localization occurs in isolated quantum systems when Anderson
localization persists in the presence of finite interactions. Despite strong
evidence for the existence of a many-body localization transition a reliable
extraction of the critical disorder strength is difficult due to a large drift
with system size in the studied quantities. In this work we explore two
entanglement properties that are promising for the study of the manybody
localization transition: the variance of the half-chain entanglement entropy of
exact eigenstates and the long time change in entanglement after a local quench
from an exact eigenstate. We investigate these quantities in a disordered
quantum Ising chain and use them to estimate the critical disorder strength and
its energy dependence. In addition, we analyze a spin-glass transition at large
disorder strength and provide evidence for it being a separate transition. We
thereby give numerical support for a recently proposed phase diagram of
many-body localization with localization protected quantum order [Huse et al.
Phys. Rev. B 88, 014206 (2013)].Comment: 4+ pages + 1.5 pages appendix, 5 figure
