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

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 $\alpha \le 2d$ 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 $0\le \alpha \le d$. 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].

To be submitted to Physical Review A

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• Slow Nonthermalizing Dynamics in a Quantum Spin Glass
• Recent progress on quantum simulations of non-standard Bose-Hubbard models
• Chaotic dynamics in a quantum Fermi-Pasta-Ulam problem
• Many-body localization regime for cavity induced long-range interacting models
• Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping