Many-body localization transition with power-law interactions: Statistics of eigenstates

K. S. Tikhonov and A. D. Mirlin
Phys. Rev. B 97, 214205 – Published 22 June 2018

Abstract

We study spectral and wave-function statistics for many-body localization transition in systems with long-range interactions decaying as 1/rα with an exponent α satisfying dα2d, where d is the spatial dimensionality. We refine earlier arguments and show that the system undergoes a localization transition as a function of the rescaled disorder W*=W/L2dαlnL, where W is the disorder strength and L the system size. This transition has much in common with that on random regular graphs. We further perform a detailed analysis of the inverse participation ratio (IPR) of many-body wave functions, exploring how ergodic behavior in the delocalized phase switches to fractal one at the critical point and on the localized side of the transition. Our analytical results for the scaling of the critical disorder W with the system size L and for the scaling of IPR in the delocalized and localized phases are supported and corroborated by exact diagonalization of spin chains.

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  • Received 19 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.214205

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

K. S. Tikhonov1,2 and A. D. Mirlin1,3,2,4

  • 1Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 2L. D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
  • 3Institut für Theorie der Kondenserten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 4Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

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Issue

Vol. 97, Iss. 21 — 1 June 2018

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