Illinois allocation proposal: Numerical study of the many body localization transition

David Luitz, University of Illinois at Urbana-Champaign

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We propose to study the nature of the many body localization transition in interacting one dimensional quantum spin chains. Previous work using the shift invert technique to obtain high energy eigenpairs of the Hamiltonian showed the energy dependence of the critical disorder strength using results for chains of lengths up to L = 22. In order to investigate the stability of this result towards the thermodynamic limit, we propose to study the time evolution of initial product states after a global quench, which is known to distinguish the localized and ergodic phases by the growth of the entanglement entropy. We have obtained preliminary results for spin chains of size L up to 28 spins (S = ½) and expect the unique oating point and memory bandwidth power of the Blue Waters machine to allow for a more precise study of even larger chains. This is crucial to respond to the open question of the existence of a subdiusive phase within the ergodic phase.