Comment on "Many-body localization in Ising models with random long-range interactions"

This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r(-alpha), relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015)] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for alpha <= 2d in a d-dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016)]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016)] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 <= alpha <= d. The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al.