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Researchers introduce a higher-dimensional Sachdev-Ye-Kitaev (SYK) model that exhibits a many-body localization (MBL) transition. This model reveals a direct dynamical transition from a diffusive metal to an MBL phase without an intermediate subdiffusive state.

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Area of Science:

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

Background:

  • Many-body localization (MBL) transitions are not fully understood.
  • The Sachdev-Ye-Kitaev (SYK) model is a key theoretical framework for studying quantum chaos.

Purpose of the Study:

  • To propose and investigate a higher-dimensional generalization of the SYK model.
  • To explore the possibility of an MBL transition in this generalized model.

Main Methods:

  • Construction of a bipartite lattice model with N Majorana fermions (SYK interactions) on sublattice A and M free Majorana fermions on sublattice B.
  • Analysis of the diffusive constant D and its behavior near a critical ratio r = M/N.
  • Numerical calculations of energy level statistics.

Main Results:

  • The model exhibits a diffusive metal phase for r < r_c = 1, characterized by maximal chaos.
  • The diffusive constant D vanishes as D ∝ (r_c - r)^1/2 as r approaches r_c, indicating a dynamical transition to an MBL phase.
  • Level statistics transition from Wigner-Dyson to Poisson distributions, confirming the MBL transition.
  • No subdiffusive phase is observed between the diffusive and MBL phases.
  • The critical exponent ν = 0 violates the Harris criterion.

Conclusions:

  • The proposed higher-dimensional SYK model provides a new platform for studying MBL transitions.
  • The direct transition from a diffusive metal to an MBL phase, bypassing a subdiffusive regime, is a significant finding.
  • The violation of the Harris criterion suggests exotic properties of this MBL transition.