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

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.

6 pages, 4 figures, references added

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