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
Summary
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.
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.
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