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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Disordered Systems

Background:

  • Many-body localization (MBL) describes the failure of thermalization in disordered quantum systems.
  • Understanding MBL transitions is crucial for quantum information and statistical mechanics.
  • Long-range hopping interactions can significantly alter localization phenomena.

Purpose of the Study:

  • To develop a real-space renormalization-group (RSRG) scheme for studying MBL transitions with long-range hopping (t∼r^{-α}).
  • To analyze the impact of interaction range on entanglement entropy and maximum block size.
  • To determine the universality classes and scaling behaviors of MBL transitions under different long-range hopping parameters.

Main Methods:

  • Development of a real-space renormalization-group (RSRG) scheme incorporating long-range hopping.
  • Analysis of entanglement entropy and maximum block size to identify localization transitions.
  • Investigation of disorder strength renormalization and finite-size scaling.

Main Results:

  • For α<2, a logarithmic dependence of renormalized disorder on system size was observed, indicating a distinct universality class.
  • For α>2, the MBL transition occurred without disorder rescaling and belonged to the same universality class as short-range models.
  • A microscopic RSRG scheme revealed power-law scaling with logarithmic corrections (α<2) and stretched exponential scaling (α>2).

Conclusions:

  • The study identifies two distinct universality classes for MBL transitions depending on the long-range hopping exponent α.
  • The MBL phase for α>2 may exhibit instability in the thermodynamic limit, despite algebraic localization.
  • The findings highlight the importance of interaction range in determining MBL properties and phase stability.