Many-body localization in a quantum Ising model with the long-range interaction: Accurate determination of the transition point

TL;DR

This paper investigates the many-body localization transition in a quantum Ising model with long-range interactions, providing an accurate estimate of the transition point and insights into critical behavior near the transition.

Contribution

It introduces a method to accurately determine the MBL transition point in a long-range interacting quantum Ising model, combining analytical estimates with numerical validation.

Findings

The transition point is consistent with estimates from Bethe lattice models.

Long-range interactions suppress local fluctuations, aiding in the detection of the transition.

Results are relevant for various physical systems with long-range interactions.

Abstract

Many-body localization (MBL) transition emerges at strong disorder in interacting systems, separating chaotic and reversible dynamics. Although the existence of MBL transition within the macroscopic limit in spin chains with a short-range interaction was proved rigorously, the transition point is not found yet because of the dramatic sensitivity of the transition point to the chain length at computationally accessible lengths, possible due to local fluctuations destroying localization. Here we investigate MBL transition in the quantum Ising model (Ising model in a transverse field) with the long-range interaction suppressing the fluctuations similarly to that for the second-order phase transitions. We estimate the MBL threshold within the logarithmic accuracy using exact results for a somewhat similar localization problem on a Bethe lattice problem and show that our expectations are fully consistent with the estimate of the transition point using exact diagonalization. In spite of unlimited growing of the critical disorder within the thermodynamic limit, this result offers the opportunity to probe the critical behavior of the system near the transition point. Moreover, the model is relevant for the wide variety of physical systems with the long-range dipole-dipole, elastic or indirect exchange interactions.