Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models

Abstract

The Sachdev-Ye-Kitaev model is a (0 + 1)-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with N Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large N limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a "butterfly velocity" describing the propagation of chaos in space. We mainly present results for a (1 + 1)-dimensional example, and discuss the general case near the end.

The bulk dual of SYK: cubic couplings

“…For instance, one can add flavor to SYK [18], leading to more refined symmetry groups and more parameters. Viewing the flavor index as a site index, one can add these flavored SYK's to form a higher-dimensional SYK [49]. Or, one can consider a Lorentz invariant higher-dimensional bosonic SYK [30].…”

Supersymmetric SYK model and random matrix theory

“…As is maximally chaotic and nearly conformal, this model could be treated as a holographic dual of quantum black hole with AdS 2 horizon through the (near) AdS/CFT correspondence [11][12][13][14][15][16][17][18][19][20]. In the recent research people have also discussed several generalizations of the SYK model [21][22][23][24], such as higher dimensional generalizations and supersymmetric constraints. Some other related issues and similar models are discussed in .…”

Higher dimensional generalizations of the SYK model

“…2 In [22], a 1+1 translationally invariant model (on average), and higher dimensional extensions, were proposed. In [23], the authors propose a generalization by introducing an extra flavour index for fermions and considering complicated interactions between them.…”