Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions

TL;DR

This paper investigates the many-body localization transition in disordered quantum spin chains with long-range interactions, using a real-space renormalization group approach to analyze the energy gap distribution and identify a critical point.

Contribution

It introduces a large-scale finite-size scaling method to study many-body localization in long-range interacting spin chains, providing evidence for a phase transition.

Findings

Identification of a critical interaction decay exponent $oldsymbol{ ext{α}_c}$

Distribution of excitation energy gaps shows a crossover at $oldsymbol{ ext{α}_c}$

Strong evidence for a many-body localization transition in the model

Abstract

While there are well established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power $\alpha$, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing $\alpha$. At $\alpha_c$ the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many body localization transition in disordered antiferromagnetic spin chains with long range interactions.