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

By Yingfei Gu, Xiao-Liang Qi, D. Stanford. 2016

434 citations recorded by the source corpus.

A bstractThe 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/a115626d777ba86e475a8c95bece2c8e6679d53b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. D. Stanford
3. V. Khemani
4. Matthew Fisher
5. Phil Saad
6. Jordan S. Cotler
7. S. Shenker
8. S. Vijay

In Condensed Matter Physics

1. A. Nahum
2. V. Khemani
3. Matthew Fisher
4. D. Huse
5. S. Vijay
6. Mike Blake
7. Hyunseok Lee
8. V. Rosenhaus

Citations in the corpus

• An introduction to the SYK model (2018, background): “Regarding flavor as a lattice site index, x, and taking sums of the flavored models, one can build lattices of SYK models [109].”
• Towards a 2d QFT analog of the SYK model (2017, methodology): “(2)Proposals for 2D generalizations of SYK with a discretized spatial dimension are given in [15, 16, 17].”
• Fermionic localization of the schwarzian theory (2017, background): “One expects this theory to be relevant at low-energies for generalizations of SYK with global symmetry [28, 29, 30, 31].”
• The bulk dual of SYK: cubic couplings (2017, background): “Viewing the flavor index as a site index, one can add these flavored SYK’s to form a higher-dimensional SYK [33].”
• A quantum hydrodynamical description for scrambling and many-body chaos (2017, methodology): “As an application of the point-wise shift symmetry we now propose a real-time effective action for the SYK chains, as discussed for example in [20, 33].”
• Universal diffusion in incoherent black holes (2016, background): “The results of [40] therefore suggest a more general validity of our proposal, and provide an exciting new context in which to explore it further.”
• A generalization of Sachdev-Ye-Kitaev (2016, background): “While this paper was being completed, [34] appeared, which considers a higher dimensional generalization of SYK.”
• Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models (2018, background): “An interesting feature of the (0 + 1)−dimensional SYK model in the large N limit [42, 47, 48, 107], as well as its higherdimensional generalizations that preserve the SYK form of the interactions [51, 52], is that they are also maximally chaotic with λL = 2πkBT/~.”