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Area of Science:

  • Quantum Field Theory
  • Condensed Matter Physics
  • Quantum Gravity

Background:

  • A universal bound on the Lyapunov exponent is proposed, with its saturation conjectured to indicate a gravity dual.
  • The dense Sachdev-Ye-Kitaev (SYK) model, involving N Majorana fermions with q-body interactions, exhibits this saturation at low temperatures.

Purpose of the Study:

  • To investigate the saturation of the Lyapunov exponent in sparse SYK models.
  • To explore the dependence of the Lyapunov exponent on sparsity and system size.
  • To provide evidence for the existence of gravity duals in sparse SYK models.

Main Methods:

  • Calculation of out-of-time-order correlators (OTOCs) for sparse SYK models with up to N=64 fermions.
  • Development of a novel quantum spin model simulation library utilizing matrix-free Krylov subspace methods on GPUs.
  • Analysis of sparsity-driven statistical fluctuations and finite size scaling.

Main Results:

  • The Lyapunov exponent shows no significant dependence on sparsity in the sparse SYK model, even near the percolation limit.
  • Strong support is found for the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK model.
  • The developed simulation library significantly reduces simulation time and memory usage.

Conclusions:

  • The saturation of the Lyapunov exponent in sparse SYK models strengthens the conjecture of a gravity dual.
  • This finding expands the class of field theories exhibiting gravity duals.
  • The computational methods developed enable efficient simulations of large quantum systems.