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

## TL;DR

This paper clarifies the conditions for many-body localization in long-range interacting quantum Ising models, resolving discrepancies between previous studies by reanalyzing the model and extending the scaling theory.

## Contribution

It reexamines prior numerical results and extends the scaling theory to small exponents, clarifying the localization behavior in long-range interacting systems.

## Key findings

- Infinite temperature states obey the dimensional constraint.
- Disagreements are due to state selection and transition interpretation.
- Scaling theory is extended for small exponents.

## Abstract

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 been earlier argued [1, 2] that this model obeys the dimensional constraint suggesting the delocalization of all finite temperature states in thermodynamic limit for $\alpha \leq 2d$ in a $d$-dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model in Ref. [3]. To resolve this controversy we reexamine the model of Ref. [3] 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 [2] is extended to small exponents $0 \leq \alpha \leq d$. Disagreements between two works are explained by the non-standard selection of investigated states in the ordered phase and misinterpretation of the localization-delocalization transition in Ref. [3].