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Numerical Evidence for Many-Body Localization in Two and Three Dimensions.

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Many-body localization (MBL) and its associated conserved quantities, ℓ-bits, are explored in higher dimensions. A new algorithm confirms MBL in 2D and 3D systems, suggesting transitions in these models.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Many-body localization (MBL) describes systems where statistical mechanics breaks down due to disorder and interactions.
  • The phenomenon is linked to quasilocal, binary conserved quantities known as ℓ-bits.
  • The existence of MBL and ℓ-bits in dimensions greater than one remains an open question.

Purpose of the Study:

  • To develop an algorithm for finding approximate binary ℓ-bits in arbitrary dimensions.
  • To investigate the presence of MBL and ℓ-bits in higher-dimensional quantum systems.

Main Methods:

  • An adaptive algorithm was developed to generate operator bases for representing ℓ-bits.
  • The algorithm was applied to 1D, 2D, and 3D disordered Heisenberg models and a 2D disordered hard-core Bose-Hubbard model.

Main Results:

  • High-quality ℓ-bits were found in all studied models at large disorder strengths.
  • Rapid changes in ℓ-bit distributions indicated potential MBL transitions.
  • Transitions in 1D and 2D models aligned with previous critical disorder strength estimates.

Conclusions:

  • The study provides evidence for MBL phenomenology in 2D and 3D systems.
  • The developed algorithm successfully probes MBL in higher dimensions and various geometries.
  • This work opens avenues for studying MBL beyond one-dimensional systems.