Many-body localization transition in random quantum spin chains with long-range interactions

¹ Department of Physics and Astronomy, University of Southern California - Los Angeles, CA 90089-0484, USA
² Department of Physics and Earth Sciences, Jacobs University Bremen - Bremen 28759, Germany
³ Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH) Pohang 790-784, South Korea

Received: 26 May 2015
Accepted: 20 July 2015

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 α, 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 α. At 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.