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Multifractal Scalings Across the Many-Body Localization Transition.

Nicolas Macé1, Fabien Alet1, Nicolas Laflorencie1

  • 1Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France.

Physical Review Letters
|November 26, 2019
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This summary is machine-generated.

Many-body localization (MBL) eigenstates are delocalized but nonergodic in Hilbert space, exhibiting multifractal behavior. The MBL transition is marked by a jump in multifractal dimensions, differing from Anderson localization.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body localization

Background:

  • Anderson localization describes real-space localization of quantum systems.
  • Many-body localization (MBL) in Hilbert space remains less understood.
  • Ergodicity properties are crucial for characterizing quantum phase transitions.

Purpose of the Study:

  • Investigate ergodicity properties of many-body localization (MBL) in Hilbert space.
  • Characterize the nature of eigenstates in delocalized and MBL phases.
  • Identify signatures of the MBL transition.

Main Methods:

  • Employed exact diagonalization techniques.
  • Analyzed N-dimensional complex networks for up to L=24 spin-1/2 particles.
  • Examined eigenstates across various computational bases.

Main Results:

  • Observed fully ergodic eigenstates in the delocalized phase, independent of the computational basis.
  • Found generically multifractal and nonergodic eigenstates in the MBL regime.
  • Identified a nonuniversal jump in multifractal dimensions signaling the MBL transition.

Conclusions:

  • MBL eigenstates exhibit basis-dependent multifractality, distinct from Anderson localization.
  • The MBL transition is characterized by a jump in multifractal dimensions.
  • This work clarifies the nature of MBL in Hilbert space.