Many-body localization edge in the random-field Heisenberg chain

Wednesday, February 11, 2015


11 février 2015, 08h31

We present a large-scale exact diagonalization study of the spin?1/2 Heisenberg chain in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to L=22 spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many-body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by GOE statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement, and nonergodicity in the Hilbert space where a true localization never occurs. We perform finite-size scaling to extract the critical edge and exponent of the localization length divergence.

Reference : David Luitz, Nicolas Laflorencie, and Fabien Alet,

Phys. Rev. B 91, 081103(R) (2015), Selected for Editors' Suggestion

 

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