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

被引:798
作者
Luitz, David J. [1 ]
Laflorencie, Nicolas [1 ]
Alet, Fabien [1 ]
机构
[1] Univ Toulouse, CNRS, IRSAMC, Phys Theor Lab, F-31062 Toulouse, France
关键词
QUANTUM CHAOS; SYSTEM;
D O I
10.1103/PhysRevB.91.081103
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We present a large-scale exact diagonalization study of the one-dimensional spin-1/2 Heisenberg model 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 Gaussian orthogonal ensemble 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.
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页数:5
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