Binary-coupling sparse Sachdev-Ye-Kitaev model: An improved model of quantum chaos and holography

The sparse version of the Sachdev-Ye-Kitaev (SYK) model reproduces essential features of the original SYK model while reducing the number of disorder parameters. In this Research Letter, we propose a further simplifi-cation of the model which we call the binary-coupling sparse SYK model. We set the nonzero couplings to be +/- 1, rather than being sampled from a continuous distribution such as Gaussian. Remarkably, this simplification turns out to be an improvement: The binary-coupling model exhibits strong correlations in the spectrum, which is the important feature of the original SYK model that leads to the quick onset of the random-matrix universality, more efficiently in terms of the number of nonzero terms. This model is better suited for analog or digital quantum simulations of quantum chaotic behavior and holographic metals due to its simplicity and scaling properties.

Automated summary

The sparse version of the Sachdev-Ye-Kitaev model reduces the number of disorder parameters while reproducing essential features of the original model. In this Research Letter, a further simplification called the binary-coupling sparse SYK model is proposed. This model sets the nonzero couplings to be +/- 1 instead of sampling from a continuous distribution. Remarkably, this simplification improves the model's performance in terms of exhibiting strong correlations in the spectrum and efficiently achieving random-matrix universality with fewer nonzero terms. Due to its simplicity and scaling properties, this model is better suited for quantum simulations of chaotic behavior and holographic metals.